Cycle decompositions of \(K_n\) and \(K_n-I\). (English) Zbl 1023.05112
J. Comb. Theory, Ser. B 81, No. 1, 77-99 (2001); corrigendum ibid. 146, 532-533 (2021).
Summary: We establish necessary and sufficient conditions for decomposing the complete graph of even order minus a \(1\)-factor into even cycles and the complete graph of odd order into odd cycles.
MSC:
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 05C38 | Paths and cycles |
| 05B30 | Other designs, configurations |
Keywords:
complete graphReferences:
| [1] | Alspach, B.; Marshall, S., Even cycle decompositions of complete graphs minus a 1-factor, J. Combin. Des., 6, 441-458 (1994) · Zbl 0846.05064 |
| [2] | Bell, E., Decomposition of \(K_n\) into cycles of length at most fifty, Ars Combin., 40, 49-58 (1995) · Zbl 0845.05073 |
| [3] | Bermond, J.-C.; Favaron, O.; Maheo, M., Hamiltonian decomposition of Cayley graphs of degree 4, J. Combin. Theory Ser. B, 46, 142-153 (1989) · Zbl 0618.05032 |
| [4] | Bermond, J.-C.; Huang, C.; Sotteau, D., Balanced cycle and circuit designs: Even cases, Ars Combin., 5, 293-318 (1978) · Zbl 0434.05020 |
| [5] | Bermond, J.-C.; Sotteau, D., Balanced cycle and circuit designs: Odd cases, Proc. Colloq. Oberhof Ilmenau, 11-32 (1978) · Zbl 0434.05020 |
| [6] | Häggkvist, R., A lemma on cycle decompositions, Ann. Discrete Math., 27, 227-232 (1985) · Zbl 0577.05045 |
| [7] | Hoffman, D. G.; Linder, C. C.; Rodger, C. A., On the construction of odd cycle systems, J. Graph Theory, 13, 417-426 (1989) · Zbl 0704.05031 |
| [8] | Linder, C. C.; Rodger, C. A., Decomposition into cycles. II. Cycle systems, (Dinitz, J. H.; Stinson, D. R., Contemporary Design Theory: A Collection of Surveys (1992), Wiley: Wiley New York), 325-369 · Zbl 0774.05078 |
| [9] | Lucas, E., Récréations Mathématiques (1892), Gauthier-Villars: Gauthier-Villars Paris |
| [10] | Šajna, M., Cycle Decompositions of \(K_n\) and \(K_n −\(I\) (July 1999), Simon Fraser University |
| [11] | Sotteau, D., Decompositions of \(K_{m, n}(K*_{m, n\) · Zbl 0463.05048 |
| [12] | Tarsi, M., Decomposition of a complete multigraph into simple paths: Nonbalanced handcuffed designs, J. Combin. Theory Ser. A, 34, 60-70 (1983) · Zbl 0511.05024 |
| [13] | Wilson, R. M., Construction and uses of pairwise balanced designs, Math. Centre Tracts, 55, 18-41 (1974) · Zbl 0312.05010 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
