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Minimal Hamiltonian graphs with prescribed degree sets. (English. Russian original) Zbl 0717.05052

Math. Notes 47, No. 4, 391-400 (1990); translation from Mat. Zametki 47, No. 4, 115-127 (1990).
See the review in Zbl 0703.05037.

MSC:

05C45 Eulerian and Hamiltonian graphs
05C35 Extremal problems in graph theory

Citations:

Zbl 0703.05037
Full Text: DOI

References:

[1] L. Lesniak, A. D. Polimeni, and D. W. Vanderjagt, ?Degree sets and traversability,? Rend. Mat.,10, No. 2-3, 193-204 (1977). · Zbl 0373.05052
[2] I. E. Zverovich, ?Realizability of a finite set of natural numbers as the set of degrees of vertices of a Hamiltonian graph,? Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat., No. 4, 32-37 (1986). · Zbl 0614.05035
[3] I. E. Zverovich, ?Degree set and traversability of a graph,? (Redkollegiya Zh. Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat., 1986). Manuscript deposited at VINITI.
[4] S. F. Kapoor, A. D. Polimeni, and C. E. Wall, ?Degree sets for graphs,? Fund. Math.,95, No. 3, 189-194 (1977). · Zbl 0351.05129
[5] R. J. Gould and D. R. Lick, ?Degree sets and graph factorizations,? Colloq. Math.,48, No. 2, 269-277 (1984). · Zbl 0559.05044
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[7] E. Ruch and I. Gutman, ?The branching extent of graphs,? J. Combin. Inform. System Sci.,4, No. 4, 285-295 (1979). · Zbl 0461.05057
[8] D. J. Kleitman and D. L. Wang, ?Algorithms for constructing graphs and digraphs with given valences and factors,? Discrete Math.,6, 79-88 (1973). · Zbl 0263.05122 · doi:10.1016/0012-365X(73)90037-X
[9] S. Kundu, ?The k-factor conjecture is true,? Discrete Math.,6, 367-376 (1973). · Zbl 0278.05115 · doi:10.1016/0012-365X(73)90068-X
[10] A. R. Rao and S. B. Rao, ?On factorable degree sequences,? J. Combinatorial Theory,B13, 185-191 (1972). · Zbl 0224.05126
[11] T. A. Sipka, ?The orders of graphs with prescribed degree sets,? J. Graph Theory,4, No. 3, 301-307 (1980). · Zbl 0442.05058 · doi:10.1002/jgt.3190040308
[12] E. F. Schmeichel and S. L. Hakimi, ?On the existence of a traceable graph with prescribed vertex degrees,? Ars. Combinatorica,4, 69-80 (1977). · Zbl 0397.05045
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