Matchings and covers in hypergraphs. (English) Zbl 0820.05051
Summary: Almost all combinatorial questions can be reformulated as either a matching or a covering problem of a hypergraph. In this paper we survey some of the important results.
MSC:
| 05C65 | Hypergraphs |
| 05-02 | Research exposition (monographs, survey articles) pertaining to combinatorics |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
References:
| [1] | Abbott, H.L., Hanson, D., Liu, A.C.: An extremal problem in graph theory. Q. J. Math. Oxford (2),31, 1–7 (1980) · Zbl 0443.05052 · doi:10.1093/qmath/31.1.1 |
| [2] | Abbott, H.L., Hanson, D., Liu, A.C.: An extremal problem in hypergraph theory. II. J. Aust. Math. Soc. (A)31, 129–135 (1981) · Zbl 0478.05070 · doi:10.1017/S1446788700033395 |
| [3] | Abbott, H.L., Hanson, D., Sauer, N.: Intersection theorems for systems of sets. J. Comb. Theory (A)12, 381–389 (1972) · Zbl 0247.05004 · doi:10.1016/0097-3165(72)90103-3 |
| [4] | Abbott, H.L., Katchalski M., Liu, A.C.: An extremal problem in hypergraph theory. In: Discrete Math. Analysis and Comb. Comp. (Conference Proceedings, School of Computer Science, Univ. New Brunswick, Fredericton 1980), pp. 74–82 · Zbl 0443.05053 |
| [5] | Abbott, H.L., Katchalski M., Liu, A.C.: An extremal problem in graph theory. II. J. Aust. Math. Soc. (A)29, 417–424 (1980) · Zbl 0443.05053 · doi:10.1017/S1446788700021571 |
| [6] | Abbott, H.L., Liu, A.: PropertyB(s) and projective planes. Ars Comb.20, 217–220 (1985) · Zbl 0597.05017 |
| [7] | Aigner, M., Erdös P., Grieser, D.: On the representing number of intersecting families. Arch. Math.49, 114–118 (1987) · Zbl 0629.05006 · doi:10.1007/BF01200473 |
| [8] | Aharoni, R.: Fractional matchings and covers in infinite hypergraphs, Combinatorica5, 181–184 (1985) · Zbl 0664.05045 · doi:10.1007/BF02579360 |
| [9] | Aharoni, R., Erdös, P., Linial, N.: Dual integer linear programs and the relationship between their optima. Proc. 17th ACM Symp. on Theory of Comput. p. 113 and 476–483 (1985) |
| [10] | Ajtai, M., Komlós, J., Rödl V., Szemerédi, E.: On coverings of random graphs. Comment. Math. Univ. Carolinae23, 193–198 (1982) |
| [11] | Alles, P.: Induced cycles in Kneser graphs. · Zbl 0688.05043 |
| [12] | Alon, N.: An extremal problem for sets with applications to graph theory. J. Comb. Theory (A)40, 82–89 (1985) · Zbl 0578.05002 · doi:10.1016/0097-3165(85)90048-2 |
| [13] | Alon N., Füredi, Z.: On the kernel of intersecting families. Graphs and Combinatorics3, 91–94 (1987) · Zbl 0651.05004 · doi:10.1007/BF01788533 |
| [14] | Alon, N., Kalai, G.: A simple proof of the upper bound theorem. Europ. J. Comb.6, 211–214 (1985) · Zbl 0582.52003 |
| [15] | Alspach, B., Ollmann, L.T., Reid, K.B.: Mutually disjoint families of 0–1 sequences. Discrete Math.12, 205–209 (1975) · Zbl 0317.05007 · doi:10.1016/0012-365X(75)90046-1 |
| [16] | Andrásfai, B.: On critical graphs. Théorie des Graphes. Rome ICC, Dunod 9–19 (1967) |
| [17] | Andrásfai, B.: Remarks on a paper of Gerencsér and Gyárfás. Ann. Univ. Sci. Eötvös, Budapest13, 103–107 (1970) |
| [18] | Bagemihl, F.: A conjecture concerning neighboring tetrahedra. Amer. Math. Mon.63, 328–329 (1956) · Zbl 0070.16009 · doi:10.2307/2310516 |
| [19] | Balinski, M. L.: Establishing the matching polytope. J. Comb. Theory (B)13, 1–13 (1972) · Zbl 0239.05137 · doi:10.1016/0095-8956(72)90002-0 |
| [20] | Balinski M.L., Spielberg, K.: Methods for integer programming: algebraic, combinatorial and enumerative. In: Progress in operations research, vol. III, Relationship between operations research and the computer. pp. 195–292. New York: Wiley, 1969 |
| [21] | Bang, C., Sharp, H., Winkler, P.: On coverings of a finite set: depth and subcovers. Period. Math. Hung.15, 51–60 (1984) · Zbl 0545.05005 · doi:10.1007/BF02109371 |
| [22] | Bassalygo L.A., Zinovèv, V.A.: Some simple corrolaries from coding theory for combinatorial problems of packings and coverings (Russian). Mat. Zametki34, 291–295 (1983) |
| [23] | Baston, V.J.D.: Some properties of Polyhedra in Euclidean Space. Oxford: Pergamon Press, 1965 · Zbl 0126.18904 |
| [24] | Beck, J.: On 3-chromatic hypergraphs. Discrete Math.24, 127–137 (1978) · Zbl 0429.05055 · doi:10.1016/0012-365X(78)90191-7 |
| [25] | Berge, C.: Sur certains hypergraphes generalisant les graphes bipartites. Comb. Th. and its Appl., Proc. Colloq. Math. Soc. J. Bolyai4, 119–133 (1970) |
| [26] | Berge, C.: Graphs and Hypergraphs. Amsterdam: North-Holland Publ. 1973 · Zbl 0254.05101 |
| [27] | Berge, C.: Balanced hypergraphs and some applications to graph theory, In: A Survey of Combinatorial Theory (J.N. Srivastava ed.), pp. 15–23 Amsterdam: North-Holland 1973 · Zbl 0264.05114 |
| [28] | Berge, C.: Regularisable graphs I and II. Discrete Math.23, 85–89 and 91–95 (1978) · Zbl 0392.05050 · doi:10.1016/0012-365X(78)90107-3 |
| [29] | Berge, C.: Packing problems and hypergraph theory: a survey. Ann. Discrete Math.4, 3–37 (1979) · Zbl 0425.05017 · doi:10.1016/S0167-5060(08)70816-1 |
| [30] | Berge, C., LasVergnas, M.: Sur un theoreme du type König pour hypergraphes. In: Proc. Int. Conf. on Combin. Math., New York 1970, pp. 32–40 · Zbl 0229.05136 |
| [31] | Berge, C., Simonovits, M.: The coloring numbers of the direct product of two hypergraphs. In: Hypergraph Seminar (Proc. First Working Seminar, Columbus, Ohio, 1972, C. Berge and D.K. Ray-Chaudhuri eds.) Lecture Notes in Math.411, pp. 21–33. Berlin: Springer-Verlag 1974 · Zbl 0321.05145 |
| [32] | Bermond, J.-C., Bollobás, B., Diameters of graphs: A survey, in ”Proc. 12th S.-E. Conf. on Combin., Graph Th. and Comput.”, Baton Rouge 1981. Congr. Numerantium32, 3–27 (1981) |
| [33] | Bermond J.-C., Bond J.: Combinatorial designs and hypergraphs of diameter one. In: Proc. First China-USA Conf. on Graph Theory, 1986 · Zbl 0792.05107 |
| [34] | Bermond, J.-C., Bond, J., Peyrat, C.: Interconnection network with each node on two buses. Parallel algorithms and architectures (Luminy 1986), pp. 155–167. Amsterdam-New York: North-Holland (1986) · Zbl 0639.94024 |
| [35] | Bermond, J.-C., Bond, J., Paoli, M., Peyrat, C.: Graphs and interconnection networks: diameter and vulnerability. In: Surveys in Combinatorics (London Math. Soc. Lecture Notes 82), edited by E.K. Lloyd, pp. 1–30. Cambridge 1983 · Zbl 0525.05018 |
| [36] | Bermond, J.-C., Bond, J., Saclé, J.F.: Large hypergraphs of diameter 1. In: Graph Theory and Combinatorics (Cambridge, 1983). pp. 19–28. London-New York: Academic Press 1984 · Zbl 0559.05043 |
| [37] | Bermond, J.-C., Delorme, C., Fahri, G.: Large graphs with given degree and diameter. II. J. Comb. Theory (B)36, 32–48 (1984) · Zbl 0539.05038 · doi:10.1016/0095-8956(84)90012-1 |
| [38] | Bermond, J.-C., Delorme, C., Fahri, G.: Large graphs with given degree and diameter. III, in Proc. Colloq. Cambridge 1981. Ann. Discrete Math.13, 23–31 (1982) · Zbl 0495.05037 |
| [39] | Beutelspacher, A.: Blocking sets and partial spreads in finite projective spaces. Geom. Dedicata9, 425–449 (1980) · doi:10.1007/BF00181559 |
| [40] | Bierbrauer, J.: Ramsey numbers for the path with three edges. Europ. J. Comb.7, 205–206 (1986) · Zbl 0606.05046 |
| [41] | Bierbrauer, J., Brandis, A.: On generalized Ramsey numbers for trees. Combinatorica5, 95–107 (1985) · Zbl 0572.05045 · doi:10.1007/BF02579372 |
| [42] | Bierbrauer J., Gyárfás, A.: On (n, k)-colorings of complete graphs. · Zbl 0656.05038 |
| [43] | Blokhuis, A.: More on maximal intersecting families of finite sets. J. Comb. Theory (A)44, 299–303 (1987) · Zbl 0608.05005 · doi:10.1016/0097-3165(87)90036-7 |
| [44] | Bollobás, B.: On generalized graphs. Acta Math. Acad. Sci. Hung.16, 447–452 (1965) · Zbl 0138.19404 · doi:10.1007/BF01904851 |
| [45] | Bollobás, B.: On a conjecture of Erdös, Hajnal and Moon. Amer. Math. Mon.74, 178–179 (1967) · Zbl 0144.45304 · doi:10.2307/2315614 |
| [46] | Bollobás, B.: Weaklyk-saturated graphs. In: Beiträge zur Graphentheorie (H. Sachs, H.-J. Voss and H. Walter, eds.), pp. 25–31. Leipzig: Teubner 1968 |
| [47] | Bollobás, B.: Graphs with given diameter and maximal valency and with a minimal number of edges. In: Combinatorial Math. and its Appl. (Proc. Conf. Oxford 1969, D.J. Welsh, ed.), pp. 25–37. London: Academic Press 1971 · Zbl 0223.05125 |
| [48] | Bollobás, B.: Extremal problems in graph theory. J. Graph Theory1, 117–123 (1977) · Zbl 0376.05041 · doi:10.1002/jgt.3190010206 |
| [49] | Bollobás, B.: Disjoint triples in a 3-graph with given maximal degree. Q. J. Math. Oxford (2)28, 81–85 (1977) · Zbl 0351.05118 · doi:10.1093/qmath/28.1.81 |
| [50] | Bollobás, B.: Extremal Graph Theory. London: Academic Press 1978 · Zbl 1099.05044 |
| [51] | Bollobás, B.: Combinatorics. Cambridge: Cambridge Univ. Press 1986 |
| [52] | Bollobás, B., Duchet, P.: Helly families of maximal size. J. Comb. Theory (A)26, 197–200 (1979) · Zbl 0411.05002 · doi:10.1016/0097-3165(79)90071-2 |
| [53] | Bollobás, B., Duchet, P.: On Helly-families of maximal size. J. Comb. Theory (B)35, 290–296 (1983) · Zbl 0539.05005 · doi:10.1016/0095-8956(83)90055-2 |
| [54] | Bollobás, B., Eldridge, S.E.: Maximal matchings in graphs with given minimal and maximal degrees. Math. Proc. Cambridge Phil. Soc.79, 221–234 (1976) · Zbl 0353.05046 · doi:10.1017/S0305004100052233 |
| [55] | Bondy, J.A., Murty, U.S.R.: Extremal graphs of diameter 2 with prescribed minimum degree. Studia Sci. Math. Hungar.7, 239–241 (1972) · Zbl 0277.05132 |
| [56] | Boros, E., Füredi, Z., Kahn, J.: Maximal intersecting families and affine regular polygons inPG(2,q). J. Comb. Theory (A) (in print) · Zbl 0737.05003 |
| [57] | Brace, A., Daykin, D.E., Cover theorems for finite sets I–III. Bull. Austral. Math. Soc.5, 197–202 (1971),6, 19–24 (1972),6, 417–433 (1972) · Zbl 0215.33001 · doi:10.1017/S0004972700047067 |
| [58] | Brouwer, A.E.: On the size of a maximum transversal in a Steiner triple system. Canad. J. Math.33, 1202–1204 (1981) · Zbl 0481.05016 · doi:10.4153/CJM-1981-090-7 |
| [59] | Brouwer A.E., Schrijver, A.: The blocking number of an affine space. J. Comb. Theory (A)24, 251–253 (1978) · Zbl 0373.05020 · doi:10.1016/0097-3165(78)90013-4 |
| [60] | Bruen, A.: Baer subplanes and blocking sets. Bull. Amer. Math. Soc.76, 342–344 (1970) · Zbl 0207.02601 · doi:10.1090/S0002-9904-1970-12470-3 |
| [61] | Bruen, A.: Blocking sets in finite projective planes. SIAM J. Appl. Math.21, 380–392 (1971) · Zbl 0252.05014 · doi:10.1137/0121041 |
| [62] | Bruen, A., Fisher, J.C.: Blocking sets,k-arcs and nets of order ten. Advances in Math.10, 317–320 (1973) · Zbl 0258.50021 · doi:10.1016/0001-8708(73)90114-X |
| [63] | Bruen A.A., de Resmini, M.J.: Blocking sets in affine planes. In: Combinatorics ’81 (Rome, 1981), North-Holland Math. Stud. 78, pp. 169–175. Amsterdam-New York: North-Holland 1983 · Zbl 0508.05021 |
| [64] | Bruen A.A., Rothschild, B.L.: Lower bounds on blocking sets. Pacific J. Math.118, 303–311 (1985) · Zbl 0571.51006 |
| [65] | Bruggesser, H., Mani, P.: Shellable decompositions of cells and spheres. Math. Scand.29, 197–205 (1971) · Zbl 0251.52013 |
| [66] | Burr, S.A., Grünbaum, B., Sloane, N.J.A.: The orchard problem. Geometriae Dedicata2, 397–424 (1974) · Zbl 0311.05024 · doi:10.1007/BF00147569 |
| [67] | Calczynska-Karlowicz, M.: Theorem on families of finite sets. Bull. Acad. Polon. Sci. Ser. Math. Astr. Phys.12, 87–89 (1964) · Zbl 0126.02401 |
| [68] | Calderbank, A.R.: Symmetric designs as the solution of an extremal problem in combinatorial set theory. Europ. J. Comb. (to appear) · Zbl 0654.05007 |
| [69] | Chung, F.R.K.: Diameters of communication networks. Proc. Symposia in Appl. Math. AMS34, 1–18 (1986) · Zbl 0595.94025 |
| [70] | Chung, F.R.K., Füredi, Z., Garey, M.R., Graham, R.L.: On the fractional covering number of hypergraphs. SIAM J. on Discrete Math. 1 (1988) (in print) · Zbl 0724.05054 |
| [71] | Chvátal, V.: Edmonds polytopes and hierarchy of combinatorial problems. Discrete Math.4, 305–337 (1973) · Zbl 0253.05131 · doi:10.1016/0012-365X(73)90167-2 |
| [72] | Chvátal, V., Hanson, D.: Degrees and matchings. J. Comb. Theory (B)20, 128–138 (1976) · Zbl 0324.05119 · doi:10.1016/0095-8956(76)90004-6 |
| [73] | Colbourn, C.J., Colbourn, M.J.: The chromatic index of cyclic Steiner 2-designs. Internat. J. Math. Sci.5, 823–825 (1982) · Zbl 0501.05011 · doi:10.1155/S0161171282000775 |
| [74] | Collins, K.L., Shor, P.W., Stembridge, J.R.: A lower bound for 0, 1, * tournament codes. Discrete Math.63, 15–19 (1987) · Zbl 0631.94014 · doi:10.1016/0012-365X(87)90147-6 |
| [75] | Csima, J.: Stochastic functions on hypergraphs. Combinatorial Theory and its Application. In: Proc. Colloq. Math. Soc. J. Bolyai 4. Amsterdam: North-Holland 1970, pp. 247–255 |
| [76] | Danzer, L., Grünbaum, B., Klee, V.: Helly’s theorem and its relatives. In: Proc. Symp. in Pure Math. 7, pp. 101–180. Providence, R.I.: Amer. Math. Soc. 1963 · Zbl 0132.17401 |
| [77] | Daykin, D.E.: Problem E 2654. Amer. Math. Monthly84, 386 (1977), Minimum subcover of a cover of a finite set (Solution of Problem E 2654). ibid85, 766 (1978) · doi:10.2307/2319978 |
| [78] | Daykin, D.E., Frankl, P.: Sets of finite sets satisfying union conditions. Mathematika (London)29, 128–134 (1982) · Zbl 0489.05004 |
| [79] | Delorme C., Fahri, G.: Large graphs with given degree and diameter. I, IEEE Trans. Comput.33, 857–860 (1984) · Zbl 0553.05042 · doi:10.1109/TC.1984.1676504 |
| [80] | Deza, M., Frankl, P.: A Helly type theorem for hypersurfaces, J. Comb. Theory (A)45, 27–30 (1987) · Zbl 0614.52008 · doi:10.1016/0097-3165(87)90043-4 |
| [81] | Dow, S.J., Drake, D.A., Füredi, Z., Larson, J.A.: A lower bound for the cardinality of a maximal family of mutually intersecting sets of equal size. Proc. 16-th S-E Conf., Congressus Numerantium48, 47–48 (1985) · Zbl 0648.05001 |
| [82] | Drake, D.A.: Maximal (k + 1)-cliques, that carry maximalk-cliques. In: Finite Geometries (Winnipeg, Manitoba, 1984) Lecture Notes in Pure and Appl. Math. 103, pp. 107–116. New York: Dekker 1985 |
| [83] | Drake, D.A.: Blocking sets in block designs. J. Comb. Theory (A)40, 459–462 (1985) · Zbl 0582.05006 · doi:10.1016/0097-3165(85)90109-8 |
| [84] | Drake, D.A.: Embedding maximal cliques of sets in maximal cliques of bigger sets. Discrete Math.58, 229–242 (1986) · Zbl 0596.05038 · doi:10.1016/0012-365X(86)90140-8 |
| [85] | Drake, D.A., Sane, S.S.: Maximal intersecting families of finite sets andn-uniform Hjelmslev planes. Proc. Amer. Math. Soc.86, 358–362 (1982) · Zbl 0504.05003 |
| [86] | Duke, R.A., Erdös, P.: A problem on complements and disjoint edges in a hypergraph. Proc. 11th Southeastern Conf. Combin., Graph Th. and Computing (Boca Raton, Fla., 1980). Congressus Numerantium28, 369–375 (1980) · Zbl 0453.05050 |
| [87] | Eckhoff, J.: An upper bound theorem for families of convex sets. Geometriae Dedicata19, 217–227 (1985) · Zbl 0588.52012 · doi:10.1007/BF00181472 |
| [88] | Edmonds. J.: Paths, trees, and flowers. Canad. J. Math.17, 449–467 (1965) · Zbl 0132.20903 · doi:10.4153/CJM-1965-045-4 |
| [89] | Edmonds, J.: Maximum matching and a polyhedron with 0, 1-vertices. J. Res. Nat. Bur. Standards Sect. B69B, 125–130 (1965) · Zbl 0141.21802 |
| [90] | Edmonds, J., Giles, R.: A min-max relation for submodular functions on graphs. Ann. Discrete Math.1, 185–204 (1977) · Zbl 0373.05040 · doi:10.1016/S0167-5060(08)70734-9 |
| [91] | Edmonds, J., Pulleyblank, W.: Facets of 1-matching polyhedra. In: Hypergraph Seminar (Proc. First Working Seminar, Columbus, Ohio, 1972, edited by C. Berge, D.K. Ray-Chaudhuri). Lecture Notes in Math. 411, pp. 214–242. Berlin: Springer 1974 · Zbl 0317.05119 |
| [92] | Ehrenfeucht, A., Mycielski, J.: Interpolation of functions over a measure space and conjectures about memory. J. Approximation Theory9, 218–236 (1973) · Zbl 0308.65008 · doi:10.1016/0021-9045(73)90089-0 |
| [93] | Erdös, P.: On a combinatorial problem II. Acta Math. Hung.15, 445–447 (1964) · Zbl 0201.33704 · doi:10.1007/BF01897152 |
| [94] | Erdös, P.: A problem of independentr-tuples. Ann. Univ. Budapest8, 93–95 (1965) |
| [95] | Erdös, P.: Problems and results in combinatorial analysis. In: Theorie Combinatorie (Roma, 1973). Acad. Naz. Lincei, Rome, 1976, vol. II, pp. 3–17 |
| [96] | Erdös, P.: Problems and results in graph theory and combinatorial analysis. In: Proc. Fifth British Combin. Conf. (1975, Aberdeen), edited by C.St.J.A. Nash-Williams et al. Congressus Numerantium 15. pp. 169–192. Winnipeg: Utilitas Math. 1976 |
| [97] | Erdös, P.: On the combinatorial problems I would most like to see solved. Combinatorica1, 25–42 (1981) · Zbl 0486.05001 · doi:10.1007/BF02579174 |
| [98] | Erdös, P., Frankl, P., Füredi, Z.: Families of finite sets in which no set is covered by the union of two others. J. Comb. Theory (A)33, 158–166 (1982) · Zbl 0489.05003 · doi:10.1016/0097-3165(82)90004-8 |
| [99] | Erdös, P., Frankl P., Füredi, Z.: Families of finite sets in which no set is covered by the union ofr others. Israel J. Math.51, 79–89 (1985) · Zbl 0587.05021 · doi:10.1007/BF02772959 |
| [100] | Erdös P., Gallai, T.: On the maximal number of vertices representing the edges of a graph. MTA Mat. Kutató Int. Közl. Budapest6, 181–203 (1961) · Zbl 0101.41001 |
| [101] | Erdös, P., Graham, R.L.: On partition theorems for finite graphs. In: Infinite and finite sets (Proc. Colloq. Math. Soc. J. Bolyai 10, Keszthely, Hungary, 1973), edited by A. Hajnal, et al. pp. 515–527. Amsterdam: North-Holland 1975 |
| [102] | Erdös, P., Hajnal, A.: On a property of families of sets. Acta Math. Hung.12, 87–123 (1961) · Zbl 0201.32801 · doi:10.1007/BF02066676 |
| [103] | Erdös, P., Hajnal, A.: On chromatic graphs (Hungarian, English summary). Mat. Lapok18, 1–4 (1967) |
| [104] | Erdös, P., Hajnal, A., Moon, J.W.: A problem in graph theory. Amer. Math. Monthly71, 1107–1110 (1964) · Zbl 0126.39401 · doi:10.2307/2311408 |
| [105] | Erdös, P., Hanani, H.: On a limit theorem in combinatorial analysis. Publ. Math. Debrecen10, 10–13 (1963) · Zbl 0122.24802 |
| [106] | Erdös, P., Kleitman, D.J.: Extremal problems among subsets of a set. Discrete Math.8, 281–294 (1974) (see also Proc. 2nd Chapel Hill Conf., Univ. North Carolina, August 1970, pp. 146–170) · Zbl 0281.04002 · doi:10.1016/0012-365X(74)90140-X |
| [107] | Erdös, P., Ko, C., Rado, R.: Intersection theorems for systems of finite sets. Quart. J. Math. Oxford (2)12, 313–320 (1961) · Zbl 0100.01902 · doi:10.1093/qmath/12.1.313 |
| [108] | Erdös, P., Lovász, L.: Problems and results on 3-chromatic hypergraphs and some related questions. In: Infinite and Finite Sets (Proc. Colloq. Math. Soc. J. Bolyai 10, Keszthely, Hungary, 1973), edited by A. Hajnal et al. pp. 609–627. Amsterdam: North-Holland 1975 |
| [109] | Erdös, P., Rado, R., Intersection theorems for systems of sets. J. London Math. Soc.35, 85–90 (1960) · Zbl 0103.27901 · doi:10.1112/jlms/s1-35.1.85 |
| [110] | Erdös, P., Rényi, A.: On a problem in the theory of graphs (in Hungarian). Magyar Tud. Akad. Mat. Kutató Int. Közl.7/A, 623–641 (1963) |
| [111] | Erdös, P., Rényi, A., Sós, V. T.: On a problem of graph theory. Studia Sci. Math. Hungar.1, 215–235 (1966) · Zbl 0144.23302 |
| [112] | Lo Faro, G.: Partial parallel classes in Steiner systemS(2, 3, 19). J. Inform. Optim. Sci.6, 133–136 (1985) · Zbl 0606.05011 |
| [113] | Fort, M.K., Jr., Hedlund, G.A.: Minimal coverings of pairs by triples. Pacific J. Math.8, 709–719 (1958) · Zbl 0084.01401 |
| [114] | Frankl, P.: On intersecting families of finite sets, J. Comb. Theory (A)24, 146–161 (1978) · Zbl 0384.05002 · doi:10.1016/0097-3165(78)90003-1 |
| [115] | Frankl, P.: On intersecting families of finite sets, Bull. Austral. Math. Soc.21, 363–372 (1980) · Zbl 0425.05002 · doi:10.1017/S0004972700006225 |
| [116] | Frankl, P.: An extremal problem for two families of sets. Europ. J. Comb.3, 125–127 (1982) · Zbl 0488.05004 |
| [117] | Frankl, P.: Asymptotic solution of a locally Turán problem. Studia Sci. Math. Hungar.19, 253–257 (1987) · Zbl 0634.05005 |
| [118] | Frankl, P.: The shifting technique in extremal set theory. Combinatorial Surveys 1987, edited by C. Whitehead, pp. 81–110. Cambridge Univ. Press 1987 · Zbl 0633.05038 |
| [119] | Frankl, P.: Erdös-Ko-Rado theorem with conditions on the maximal degree. J. Comb. Theory (A)46, 252–263 (1987) · Zbl 0661.05002 · doi:10.1016/0097-3165(87)90005-7 |
| [120] | Frankl, P., Füredi, Z.: Disjointr-tuples in anr-graph with given maximum degree. Quart. J. Math. Oxford (2)34, 423–426 (1983) · Zbl 0543.05049 · doi:10.1093/qmath/34.4.423 |
| [121] | Frankl, P., Füredi, Z.: Finite projective spaces and intersecting hypergraphs. Combinatorica6, 335–354 (1986) · Zbl 0643.05018 · doi:10.1007/BF02579260 |
| [122] | Frankl, P., Füredi, Z.: Non-trivial intersecting families. J. Comb. Theory (A)41, 150–153 (1986) · Zbl 0583.05002 · doi:10.1016/0097-3165(86)90121-4 |
| [123] | Frankl, P., Füredi, Z.: Colored packing of sets in combinatorial design theory. Annals of Discrete Math.34, 165–178 (1987) · Zbl 0675.05020 |
| [124] | Frankl, P., Pach, J.: On disjointly representable sets. Combinatorica4, 39–45 (1984) · Zbl 0534.05003 · doi:10.1007/BF02579155 |
| [125] | Frankl, P., Rödl, V.: Near perfect coverings in graphs and hypergraphs. Europ. J. Comb.6, 317–326 (1985) · Zbl 0624.05055 |
| [126] | Frankl, P., Stečkin, B.S.: In: Combinatorial Analysis, Problems and Exercises (in Russian). Problem 6.41. Moscow: Nauka 1982 |
| [127] | Fulkerson, D.R.: Blocking and anti-blocking pairs of polyhedra. Math. Progr.1, 168–194 (1971) · Zbl 0254.90054 · doi:10.1007/BF01584085 |
| [128] | Füredi, Z.: On maximal intersecting families of finite sets. J. Comb. Theory (A)28, 282–289 (1980) · Zbl 0438.05002 · doi:10.1016/0097-3165(80)90071-0 |
| [129] | Füredi, Z.: Erdös-Ko-Rado type theorems with upper bounds on the maximum degree. In: Algebraic Methods in Graph Theory (Szeged, Hungary, 1978), Proc. Colloq. Math. Soc. J. Bolyai. 25, edited by L. Lovász et al. pp. 177–207. Amsterdam: North-Holland 1981 |
| [130] | Füredi, Z.: Maximum degree and fractional matchings in uniform hypergraphs. Combinatorica1, 155–162 (1981) · Zbl 0494.05045 · doi:10.1007/BF02579271 |
| [131] | Füredi, Z.: An intersection problem with 6 extremes. Acta. Math. Hungar.42, 177–187 (1983) · Zbl 0538.05002 · doi:10.1007/BF01956765 |
| [132] | Füredi, Z.: Geometrical solution of an intersection problem for two hypergraphs. Europ. J. Comb.5, 133–136 (1984) · Zbl 0546.05048 |
| [133] | Füredi, Z.:t-expansive andt-wise intersecting hypergraphs. Graphs and Combinatorics2, 67–80 (1986) · Zbl 0594.05050 · doi:10.1007/BF01788079 |
| [134] | Füredi, Z.: Onr-graphs andr-multihypergraphs with given maximum degree. J. Austral Math. Soc. A (submitted) · Zbl 0762.05084 |
| [135] | Füredi, Z.: Covering pairs byq 2 + q + 1 sets. J. Comb. Theory (A) (submitted) · Zbl 0734.05033 |
| [136] | Füredi, Z.: Covering the complete graph by partitions. Discrete Math. (submitted) · Zbl 0704.05018 |
| [137] | Füredi, Z.: Kahn, J., Seymour, P.: On the fractional matching polytope of hypergraphs. (prepared) · Zbl 0779.05030 |
| [138] | Füredi, Z., Palásti, I.: Arrangements of lines with a large number of triangles. Proc. Amer. Math. Soc.92, 561–566 (1984) · Zbl 0521.51003 |
| [139] | Füredi, Z., Tuza, Zs.: Hypergraphs without a large star. Discrete Math.55, 317–321 (1985) · Zbl 0569.05042 · doi:10.1016/S0012-365X(85)80009-1 |
| [140] | Gale, D.: Neighborly and cyclic polytopes. In: Proc. Sympos. Pure Math. VII (Seattle, 1961), pp. 225–232. Providence, RI: Amer. Math. Soc. 1963 |
| [141] | Gallai, T.: Neuer Beweis eines Tutteschen Satzes. MTA Mat. Kut. Int. Közl.8, 135–139 (1963) · Zbl 0129.39802 |
| [142] | Gerencsér, L., Gyárfás, A.: On Ramsey-type problems. Ann. Univ. Sci. Eötvös, Budapest10, 167–170 (1967) |
| [143] | Gomory, R.: An algorithm for integer solutions of linear programs. In: Recent Advances in Math. Prog., pp. 269–302. New York: McGraw-Hill 1963 · Zbl 0235.90038 |
| [144] | Graham, R.L.: Private communication |
| [145] | Grünbaum, B.: Convex Polytopes. London: Wiley-Interscience 1967 · Zbl 0163.16603 |
| [146] | Griggs, J.R., Stahl, J., Trotter, W.T., Jr.: A Sperner theorem on unrelated chains of subsets. J. Comb. Theory (A)36, 124–127 (1984) · Zbl 0526.05002 · doi:10.1016/0097-3165(84)90085-2 |
| [147] | Gyárfás, A. Partition covers and blocking sets in hypergraphs (in Hungarian). MTA SZTAKI Tanulmányok 71. Budapest 1977 |
| [148] | Gyárfás, A., Lehel, J., Tuza, Zs.: Upper bound on the order of{\(\tau\)}-critical hypergraphs. J. Comb. Theory (B)33, 161–165 (1982) · Zbl 0498.05050 · doi:10.1016/0095-8956(82)90065-X |
| [149] | Haemers, W.: Eigenvalue methods. Math. Centre Tracts106, 15–38 (1979) · Zbl 0438.05035 |
| [150] | Hajnal, A.: A theorem onk-saturated graphs. Canad. J. Math.17, 720–724 (1965) · Zbl 0129.39901 · doi:10.4153/CJM-1965-072-1 |
| [151] | Hansen, P., Lorea, M.: Le nombre de transversalité du plan affine á 49 sommets. In: Analyse appliquée et informatique, edited by J.-C. Bermond, R. Cori, pp. 201–209. Bordeaux 1975 · Zbl 0357.05032 |
| [152] | Hanson, D., Toft, B.: On the maximum number of vertices inn-uniform cliques. Ars Combinatoria16A, 205–216 (1983) · Zbl 0555.05056 |
| [153] | Halberstam H., Roth, K.F.: Sequences. London: Oxford 1966 · Zbl 0141.04405 |
| [154] | Hartman, A., Mills W.H., Mullin, R.C.: Covering triples by quadruples, an asymptotic solution. J. Comb. Theory (A)41, 117–138 (1986) · Zbl 0587.05022 · doi:10.1016/0097-3165(86)90119-6 |
| [155] | Hemmeter, J., Hong, Y.: Sparse matchings in the Johnson GraphJ(n, k) |
| [156] | Hilton, A.J.W., Milner, E.C.: Some intersection theorems for systems of finite sets. Quart. J. Math. Oxford (2)18, 369–384 (1967) · Zbl 0168.26205 · doi:10.1093/qmath/18.1.369 |
| [157] | Hirschfeld, J.W.P.: Projective Geometry over Finite Fields. Oxford: Clarendon Press 1979 · Zbl 0418.51002 |
| [158] | Hoffman, A.J.: A generalization of max flow-min cut. Math. Progr.6, 352–359 (1974) · Zbl 0357.90068 · doi:10.1007/BF01580250 |
| [159] | Jaeger, F., Payan, C.: Nombre maximal d’arétes d’un hypergraphe critique de rangh. C.R. Acad. Sci. Paris273, 221–223 (1971) · Zbl 0234.05119 |
| [160] | Jamison, R.E.: Covering finite fields with cosets of subspaces. J. Comb. Theory (A)22, 253–266 (1977) · Zbl 0354.12019 · doi:10.1016/0097-3165(77)90001-2 |
| [161] | Jungnickel, D., Leclerc, M.: Blocking sets in (r, {\(\lambda\)})-designs. Ars Combinatoria22, 211–219 (1986) · Zbl 0608.05013 |
| [162] | Kalai, G.: Intersection patterns of convex sets. Israel J. Math.48, 161–174 (1984) · Zbl 0557.52005 · doi:10.1007/BF02761162 |
| [163] | Katona, G.O.H.: Solution of a problem of Ehrenfeucht and Mycielski. J. Comb. Theory (A)17, 265–266 (1974) · Zbl 0289.05002 · doi:10.1016/0097-3165(74)90018-1 |
| [164] | Katona, G., Szemerédi, E.: On a problem of graph theory. Studia Sci. Math. Hungar.2, 23–28 (1967) · Zbl 0147.42804 |
| [165] | Kelly, D., Trotter, W.T., Jr.: Dimension theory for ordered sets. In: Ordered Sets (Banff, Alberta, 1981). NATO Advanced Study Inst. Ser. C 83, pp. 171–211. Dordrecht-Boston: Reidel 1982 |
| [166] | Kitto, C.: A bound for blocking sets of maximal type in finite projective planes. · Zbl 0636.51010 |
| [167] | Kleitman, D. (Peck, G.W.), Paoli, M., Trotter, W.T., Jr., West, D.B.: The maximum number of edges in regular 2K 2-free graphs (manuscript) |
| [168] | Kuzyurin, N.N.: One limit theorem about (n, k, l)-coverings. Discrete Math. and its Appl. to Math. Cybernetics, III (Rostock, 1981), Rostock. Math. Kolloq.21, 59–62 (1982) |
| [169] | Laskas, R., Sherk, F.A.: Generating sets in finite projective planes. In: Finite Geometries, edited by C. Baker, L.M. Batten (Proc. Conf. Finite Geometries. Winnipeg, 1984 Lecture Notes in Pure and Appl. Math. 103, pp. 183–198. M. Dekker Publ. Co., 1985 |
| [170] | Lehel, J.:{\(\tau\)}-critical hypergraphs and the Helly-property. Ann. Discrete Math.17, 413–418 (1982) · Zbl 0522.05052 |
| [171] | Lehel, J.: Multitransversals in{\(\tau\)}-critical hypergraphs. In: Finite and Infinite Sets (Proc. Colloq. Math. Soc. J. Bolyai 37, Eger, Hungary, 1981), pp. 567–576. Amsterdam: North-Holland 1984 |
| [172] | van Lint, J.H.: {0, 1, *} distance problems in combinatorics. In: Surveys in Combinatorics, edited by I. Anderson. London Math Soc. Lecture Notes 103, pp. 113–135. Cambridge Univ. Press 1985 · Zbl 0581.94019 |
| [173] | Lorentz, G.G.: On a problem in additive number theory. Proc. Amer. Math. Soc.5, 838–841 (1954) · Zbl 0056.03902 · doi:10.1090/S0002-9939-1954-0063389-3 |
| [174] | Lovász, L.: Normal hypergraphs and the perfect graph conjecture. Discrete Math.2, 253–267 (1972) · Zbl 0239.05111 · doi:10.1016/0012-365X(72)90006-4 |
| [175] | Lovász, L.: Minimax theorems for hypergraphs. In: Hypergraph Seminar. Lecture Notes in Math. 411, pp. 111–126. Berlin: Springer 1974 · Zbl 0305.05129 |
| [176] | Lovász, L.: On the ratio of optimal integral and fractional covers. Discrete Math.13, 383–390 (1975) · Zbl 0323.05127 · doi:10.1016/0012-365X(75)90058-8 |
| [177] | Lovász, L.: On minimax theorems of combinatorics (Doctoral thesis, in Hungarian). Mathematikai Lapok26, 209–264 (1975) · Zbl 0397.05040 |
| [178] | Lovász, L.: 2-matchings and 2-covers of hypergraphs. Acta Math. Hungar.26, 433–444 (1975) · Zbl 0339.05123 · doi:10.1007/BF01902352 |
| [179] | Lovász, L.: On two minimax theorems in graph theory. J. Comb. Theory (B)21, 96–103 (1976) · Zbl 0337.05115 · doi:10.1016/0095-8956(76)90049-6 |
| [180] | Lovász, L.: Covers, packings and some heuristic algorithms. In: Proc. 5th British Comb. Conf., Congressus Numerantium 15, Utilitas Math., Winnipeg, 1976, pp. 417–429 · Zbl 0353.05027 |
| [181] | Lovász, L.: Flats in matroids and geometric graphs. In: Combinatorial Surveys (Proc. 6th British Combin. Conf.) edited by P.J. Cameron, pp. 45–86. New York: Academic Press 1977 · Zbl 0361.05027 |
| [182] | Lovász, L.: Certain duality principles in integer programming. Ann. Discrete Math.1, 363–374 (1977) · Zbl 0358.90046 · doi:10.1016/S0167-5060(08)70744-1 |
| [183] | Lovász, L.: Some finite basis theorems in graph theory. In: Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely 1976). Proc. Colloq. Math. Soc. J. Bolyai 18, pp. 717–729. Amsterdam: North-Holland 1978 |
| [184] | Lovász, L.: Graph theory and integer programming. Discrete Optimization (Proc. Adv. Res. Inst. Discrete Optimization and Systems Appl., Banff, Alberta, 1977). Annals of Discrete Math.4, 141–158 (1979) · Zbl 0407.05053 · doi:10.1016/S0167-5060(08)70822-7 |
| [185] | Lovász, L.: Topological and algebraic methods in graph theory. In: Graph Theory and Related Topics (Proc. of Tutte Conf., Waterloo, 1977), edited by J.A. Bondy and U.S.R. Murty, pp. 1–15. New York: Academic Press 1979 |
| [186] | Lovász, L.: Combinatorial Problems and Exercises. Budapest: Akadémiai Kiadó, Budapest/Amsterdam: North-Holland 1979 |
| [187] | Lovász, L.: On the Shannon capacity of a graph. IEEE Trans. Inform. Theory25, 1–7 (1979) · Zbl 0395.94021 · doi:10.1109/TIT.1979.1055985 |
| [188] | Lovász, L.: Plummer, M.D.: Matching Theory. Annals of Discrete Math.29, Amsterdam: North-Holland (1986) · Zbl 0618.05001 |
| [189] | Jia Xi Lu: On large sets of disjoint Steiner triple systems I, II and III. J. Comb. Theory (A)34, 140–146, 147–155, 156–182 (1983) · Zbl 0514.05018 · doi:10.1016/0097-3165(83)90052-3 |
| [190] | Marcus, M.: Finite Dimensional Multilinear Algebra. New York: Dekker 1975 · Zbl 0339.15003 |
| [191] | McEliece, R.J., Posner, E.C.: Hide and seek, data storage, and entropy. Amer. Statist.42, 1706–1716 (1971) · Zbl 0235.05001 |
| [192] | McMullen, P.: The maximum numbers of faces of a convex polytope. Mathematika17, 179–184 (1970) · Zbl 0217.46703 · doi:10.1112/S0025579300002850 |
| [193] | Meyer, J.-C.: Quelques problémes concernant les cliques des hypergraphesh-complets etq-partih-complets. In: Hypergraph Seminar (held in Columbus, Ohio, 1972), edited by C. Berge et al. Lecture Notes in Math. 411, pp. 127–139. New York-Berlin: Springer 1974 |
| [194] | Meyer, J.-C.: 23rd unsolved problem. In: Hypergraph Seminar (held in Columbus, Ohio, 1972), edited by C. Berge et al. Lecture Notes in Math. 411, pp. 285–286. New York-Berlin: Springer 1974 |
| [195] | Mills, W.H.: On the covering of pairs by quadruples, I. J. Comb. Theory (A)13, 55–78 (1972) · Zbl 0243.05024 · doi:10.1016/0097-3165(72)90008-8 |
| [196] | Mills, W.H.: On the covering of pairs by quadruples, II. J. Comb. Theory (A)15, 138–166 (1973) · Zbl 0261.05022 · doi:10.1016/S0097-3165(73)80003-2 |
| [197] | Mills, W.H.: Covering designs I: covering by a small number of subsets. Ars Combinatoria8, 199–315 (1979) · Zbl 0445.05041 |
| [198] | Mills, W.H.: A covering of pairs by quintuples. Ars Combinatoria18, 21–31 (1984) · Zbl 0554.05017 |
| [199] | Mills W.H., Mullin, R.C.: Covering pairs by quintuples: the casev 3 (mod 4). (prepared) · Zbl 0666.05023 |
| [200] | Motzkin, T.S.: Comonotone curves and polyhedra, Abstr. 111. Bull. Amer. Math. Soc.63, 35 (1957) · doi:10.1090/S0002-9904-1957-10103-7 |
| [201] | Motzkin, T.S., Straus, E.G.: Maxima for graphs and a new proof of a theorem of Turán. Canad. J. Math.17, 533–540 (1965) · Zbl 0129.39902 · doi:10.4153/CJM-1965-053-6 |
| [202] | Mouyart, A.F., Sterboul, F.: Decomposition of the complete hypergraph into delta-systems, I. J. Comb. Theory (A)40, 290–304 (1985) · Zbl 0588.05032 · doi:10.1016/0097-3165(85)90092-5 |
| [203] | Mouyart, A.F., Sterboul, F.: Decomposition of the complete hypergraph into delta-systems, II. J. Comb. Theory (A)41, 139–149 (1986) · Zbl 0588.05033 · doi:10.1016/0097-3165(86)90120-2 |
| [204] | Mulder, H.M.: The number of edges in ak-Helly hypergraph (Proc. Colloq. Marseille-Luminy, 1981, edited by C. Berge et al.) Annals of Discrete Math.17, 497–501 (1983) · Zbl 0522.05051 |
| [205] | Nemhauser, G.L., Trotter, L.E., Jr.: Properties of vertex packing and independence system polyhedra. Math. Progr.6, 48–61 (1974) · Zbl 0281.90072 · doi:10.1007/BF01580222 |
| [206] | Pach, J., Surányi, L.: On graphs of diameter 2. Ars Combinatoria11, 61–78 (1981) |
| [207] | Pach, J., Surányi, L.: Graphs of diameter 2 and linear programming. In: Algebraic Methods in Graph Theory, edited by L. Lovász et al. (Proc. Colloq. Math. Soc. J. Bolyai, 25, Szeged, Hungary 1978), pp. 599–629. Amsterdam: North-Holland 1981 |
| [208] | Pelikán, J.: Properties of balanced incomplete block designs. In: Combinatorial Theory and its Appl, Colloq. Math. Soc. J. Bolyai 4 (Balatonfüred, Hungary 1969), pp. 869–889. Amsterdam: North-Holland 1970 |
| [209] | Perles, M.A. (written by Zaks, J.): At most 2 d+1 neighborly simplices inE d. In: Proc. Colloq. on Convexity, Israel, March 1981, edited by M. Rosenfeld et al. Annals of Discrete Math.20, 253–254 (1984) |
| [210] | Petruska, Gy., Szemerédi, E.: On a combinatorial problem 1. Studia Sci. Math. Hungar.7, 363–374 (1972) · Zbl 0302.05002 |
| [211] | Pin, J.-E.: On two combinatorial problems arising from automata theory. In: Proc. Colloq. Marseille-Luminy, 1981, edited by C. Berge et al. Annals of Discrete Math.17, 535–548 (1983) · Zbl 0523.68042 |
| [212] | Pippenger, N., Spencer, J.: Asymptotic packing and edgecoloring of near regular hypergraphs (prepared) |
| [213] | Plummer, M.D.: On a family of line-critical graphs. Monatsh. Math.71, 40–48 (1967) · Zbl 0166.19903 · doi:10.1007/BF01299958 |
| [214] | De Resmini, M.J.: On blocking sets in symmetric BIBD’s with{\(\lambda\)} 2. J. Geometry18, 194–198 (1982) · Zbl 0494.05006 · doi:10.1007/BF01947651 |
| [215] | De Resmini, M.J.: On 2-blocking sets in projective planes. In: Proc. 10th British Comb. Conf. Glasgow, 1985. Ars Combinatoria20B, 59–69 (1985) · Zbl 0607.51006 |
| [216] | De Resmini, M.J.: On 3-blocking sets in projective planes. In: Combinatorial Design Theory. Annals of Discrete Math.34 (1987) · Zbl 0636.51009 |
| [217] | Rödl, V.: On a packing and covering problem. Europ. J. Comb.6, 69–78 (1985) · Zbl 0565.05016 |
| [218] | Rosenfeld, M.: On a problem of C.E. Shannon in graph theory. Proc. Amer. Math. Soc.18, 315–319 (1967) · Zbl 0147.42801 · doi:10.1090/S0002-9939-1967-0207590-3 |
| [219] | Roudneff, J.-P.: Private communication (1986) |
| [220] | Ryser, H.J.: An extension of a theorem of deBruijn and Erdös on combinatorial designs. J. Algebra10, 246–261 (1968) · Zbl 0167.28001 · doi:10.1016/0021-8693(68)90099-9 |
| [221] | Sane, S.S.: An extremal property of the 4-(23, 7, 1) design. In: Proc. 16th S.-E. Conf. Combin., Graph Th, and Comp. Boca Raton, Fla 1985. Congressus Numerantium49, 191–193 (1985) |
| [222] | Sauer, N.: The largest number of edges of a graph such that not more thang intersect at a point and not more thann are independent. In: Combinatorial Math. and Appl. (Proc. Conf. Oxford 1969), edited by D.J. Welsh, pp. 253–257. London: Academic Press 1971 |
| [223] | Schönheim, J.: On coverings. Pacific J. Math.14, 1405–1411 (1964) · Zbl 0128.24501 |
| [224] | Schrijver, A., Seymour, P.D.: Solution of two fractional packing problems of Lovász. Discrete Math.26, 177–184 (1979) · Zbl 0413.05044 · doi:10.1016/0012-365X(79)90122-5 |
| [225] | Shiloach, Y., Vishkin, U., Zaks, S.: Golden ratios in a pairs covering problem. Discrete Math.41, 57–65 (1982) · Zbl 0489.05021 · doi:10.1016/0012-365X(82)90082-6 |
| [226] | Sperner, E.: Ein Satz über Untermengen einer endlichen Menge. Math. Z.27, 544–548 (1928) · JFM 54.0090.06 · doi:10.1007/BF01171114 |
| [227] | Spencer, J.: Coloringn-sets red and blue. J. Comb. Theory (A)30, 112–113 (1981) · Zbl 0448.05032 · doi:10.1016/0097-3165(81)90045-5 |
| [228] | Spencer, J.: Asymptotically good coverings. Pacific J. Math.118, 575–586 (1985) · Zbl 0578.05010 |
| [229] | Stein, S.K.: Two combinatorial covering theorems. J. Comb. Theory (A)16, 391–397 (1974) · Zbl 0287.05002 · doi:10.1016/0097-3165(74)90062-4 |
| [230] | Surányi, L.: On line critical graphs. In: Infinite and Finite Sets, edited by A. Hajnal et al. (Proc. Colloq. Math. Soc. J. Bolyai 10, Keszthely, Hungary 1973), pp. 1411–1444. Amsterdam: North-Holland 1975 |
| [231] | Surányi, L.: Large{\(\alpha\)}-critical graphs with small deficiency (On line-critical graphs II). Studia Sci. Math. Hungar.10, 397–412 (1975) · Zbl 0468.05061 |
| [232] | Szemerédi, E., Tuza, Zs.: Upper bound for transversals of tripartite hypergraphs. Period. Math. Hungar.13, 321–323 (1982) · Zbl 0513.05044 · doi:10.1007/BF01849243 |
| [233] | Tarján, T.: Complexity of lattice-configurations. Studia Sci. Math. Hungar.10, 203–211 (1975) |
| [234] | Todorov, D.T.: Some coverings derived from finite planes. In: Finite and Infinite Sets (Proc. Colloq. Math. Soc. J. Bolyai 37, Eger, Hungary 1981) pp. 697–710. Amsterdam: North-Holland 1984 |
| [235] | Todorov, D.T.: On the covering of pairs by 13 blocks. C.R. Acad. Bulgare Sci.38, 691–694 (1985) · Zbl 0577.05013 |
| [236] | Tutte, W.T.: The 1-factors of oriented graphs. Proc. Amer. Math. Soc.4, 922–931 (1953) · Zbl 0052.20004 |
| [237] | Tuza, Zs.: Some special cases of Ryser’s conjecture (preprint 1978) |
| [238] | Tuza, Zs.: Ryser’s conjecture on transversals ofr-partite hypergraphs. Ars Combin.16B, 201–209 (1983) · Zbl 0555.05054 |
| [239] | Tuza, Zs.: Helly-type hypergraphs and Sperner families. Europ. J. Comb.5, 185–187 (1984) · Zbl 0541.05046 |
| [240] | Tuza, Zs.: Critical hypergraphs and intersecting set-pair systems. J. Comb. Theory (B)39, 134–145 (1985) · Zbl 0586.05029 · doi:10.1016/0095-8956(85)90043-7 |
| [241] | Tuza, Zs.: Inequalities for two-set systems with prescribed intersections. Graphs and Combinatorics3, 75–80 (1987) · Zbl 0622.05006 · doi:10.1007/BF01788531 |
| [242] | Vrto, I., Znám, Š.: Minimal graphs of diameter two and given maximal degree. Studia Sci. Math. Hungar.17 (1982), 283–290 (1985) |
| [243] | Wessel, W.: Über eine Klasse paarer Graphen, I.: Beweis einer Vermutung von Erdös, Hajnal, und Moon. Wiss. Z. Tech. Hochsch. Ilmenau12, 253–256 (1966) · Zbl 0148.18004 |
| [244] | Wettl, F.: On the nuclei of a pointset of a finite projective plane. Journal of Geometry30, 157–163 (1987) · Zbl 0629.51017 · doi:10.1007/BF01227813 |
| [245] | Wilson, R.M.: An existence theory for pairwise balanced designs I–III. J. Comb. Theory (A)13, 220–273 (1972),18, 71–79 (1975) · Zbl 0263.05014 · doi:10.1016/0097-3165(72)90028-3 |
| [246] | Wilson, R.M.: Decomposition of complete graphs into subgraphs isomorphic to a given graph. In: Proc. 5th British Comb. Conf., Aberdeen, 1975. Congressus Numerantium XV, pp. 647–659. Winnipeg: Utilitas Math. 1976 |
| [247] | Zaks, J.: Bounds of neighborly families of convex polytopes. Geometriae Dedicata8, 279–296 (1979) · Zbl 0418.52012 · doi:10.1007/BF00151512 |
| [248] | Zaks, J.: Neighborly families of 2 d d-simplices inE d. Geometriae Dedicata11, 505–507 (1981) · Zbl 0469.51016 · doi:10.1007/BF00181209 |
| [249] | Zaks, J.: No nine neighborly tetrahedra exists. In: Lecture on 1986 Summer Research Conf. on Discrete and Comput. Geometry, Santa Cruz, Calif., July 1986 Discrete Math. (to appear) · Zbl 0723.52004 |
| [250] | Zaks, J.: Neighborly families of congruent convex polytopes. Amer. Math. Monthly94, 151–155 (1987) · Zbl 0617.52008 · doi:10.2307/2322415 |
| [251] | Znám, S.: Minimal graphs of diameter two. Studia Sci. Math. Hungar.19, 187–191 (1987) · Zbl 0622.05038 |
| [252] | Aharoni, R.: Matchings inn-partiten-graphs. Graphs and Combinatorics1, 303–304 (1985) · Zbl 0614.05042 · doi:10.1007/BF02582958 |
| [253] | Bierbrauer, J.: On the weight distribution in binary codes generated by projective planes. Quart. J. Math. Oxford (2)33, 275–279 (1982) · Zbl 0498.94008 · doi:10.1093/qmath/33.3.275 |
| [254] | Boros, E.: Blocking sets on Galois planes with small line intersection. Ars Combinatoria (to appear) |
| [255] | Chung, F.R.K., Gyárfás, A., Trotter, W.T., Jr., Tuza, Zs.: The maximum number of edges in 2K 2-free graphs of bounded degree. (manuscript) |
| [256] | Erdös, P., Rothschild, B., Szemerédi, E.: see in [95] or in [114] |
| [257] | Erdös, P., Silverman, R., Stein, A.: Intersection properties of families containing sets of nearly the same size. Ars Combinatoria15, 247–259 (1983) · Zbl 0521.05004 |
| [258] | Fernandez de la Vega, W.: Sur la cardinalite maximum des couplages d’hypergraphes aleatories uniformes. Discrete Math.40, 315–318 (1982) · Zbl 0488.05051 · doi:10.1016/0012-365X(82)90130-3 |
| [259] | Finkelstein, L., Kleitman, D., Leighton, T.: Applying the classification theorem for finite simple groups to minimize pin count in uniform permutation architectures. (manuscript) · Zbl 0659.20012 |
| [260] | Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completness. San Francisco, CA: Freeman (1979) · Zbl 0411.68039 |
| [261] | Geréb, M.: private communication |
| [262] | Hochbaum, D.S.: On the fractional solution to the set covering problem. SIAM J. Alg. Disc. Math.4, 221–222 (1983) · Zbl 0518.90055 · doi:10.1137/0604023 |
| [263] | Ivaniec, H., Pintz, J.: Primes in short intervals. Monatsh. Math.98, 115–143 (1984) · Zbl 0544.10040 · doi:10.1007/BF01637280 |
| [264] | Kahn, J., Seymour, P.: private communication |
| [265] | Lamken, E.R., Mills, W.H., Mullin, R.C., Vanstone, S.A.: Covering of pairs by quintuples. J. Combinatorial Theory (A)44, 49–68 (1987) · Zbl 0651.05025 · doi:10.1016/0097-3165(87)90059-8 |
| [266] | Lamken, E.R., Mullin, R.C., Vanstone, S.A.: Some non-existence results on twisted planes related to minimum covers. Congr. Numerantium48, 265–275 (1985) · Zbl 0622.05014 |
| [267] | Razborov, A.A.: Lower bounds on the monotone complexity of some Boolean functions. (Russian) Dokl. Akad. Nauk. USSR281, 798–801 (1985) · Zbl 0621.94027 |
| [268] | Rogers, M.J., Stanton, R.G.: Packing and covering by triples. Ars Combinatoria13, 61–69 (1982) · Zbl 0501.05023 |
| [269] | Tazawa, S., Yamamoto, S.: Hyperclaw decomposition of complete hypergraphs. Annals of Discrete Math.6, 385–391 (1980) · Zbl 0458.05047 · doi:10.1016/S0167-5060(08)70720-9 |
| [270] | Tuza, Zs.: Conjecture in ”Finite and Infinite Sets” (Proc. Colloq. Math. Soc. J. Bolyai 37, Eger, Hungary, 1981) p. 888. Amsterdam: North-Holland (1984) |
| [271] | Tuza, Zs.: Intersection properties and extremal problems for set systems. In Irregularities of Partitions (Sós, V.T., ed.) (Proc. Colloq. Math. Soc. J. Bolyai, Sopron, Hungary, 1986) (to appear) |
| [272] | Tuza, Zs.: A conjecture on triangles of graphs. (manuscript) · Zbl 0584.05042 |
| [273] | Tuza, Zs.: On the order of vertex sets meeting all edges of a 3-partite hypergraph. Ars Combinatoria (to appear) · Zbl 0653.05052 |
| [274] | Tuza, Zs.: Maximum number of vertices in{\(\tau\)}-critical hypergraphs. (manuscript) · Zbl 0584.05042 |
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