×

Cycle decompositions. III: Complete graphs and fixed length cycles. (English) Zbl 1033.05078

Summary: We show that the necessary conditions for the decomposition of the complete graph of odd order into cycles of a fixed even length and for the decomposition of the complete graph of even order minus a 1-factor into cycles of a fixed odd length are also sufficient.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C38 Paths and cycles

Citations:

Zbl 1022.05061
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alspach, J Combin Theory Ser B 81 pp 77– (2001) · Zbl 1023.05112 · doi:10.1006/jctb.2000.1996
[2] Alspach, Ann. Discrete Math 9 pp 155– (1980) · Zbl 0454.05041 · doi:10.1016/S0167-5060(08)70053-0
[3] Decomposition of a complete graph into cycles of length less than or equal to 50, M.Sc. thesis, Auburn University, 1991.
[4] Bermond, J Combin Theory Ser B 46 pp 142– (1989) · Zbl 0618.05032 · doi:10.1016/0095-8956(89)90040-3
[5] El-Zanati, Discrete Math 131 pp 91– (1994) · Zbl 0806.05055 · doi:10.1016/0012-365X(94)90375-1
[6] Hoffman, J Graph Theory 13 pp 417– (1989) · Zbl 0704.05031 · doi:10.1002/jgt.3190130405
[7] Kotzig, Mat-Fiz ?as 15 pp 227– (1965)
[8] ?Decomposition into cycles II: Cycle systems,? in Contemporary Design Theory: A Collection of Surveys, and (Editors), Wiley, New York, 1992, pp. 325-369.
[9] Rodger, Le Matematische 45 pp 119– (1990)
[10] Rosa, Mat-Fyz ?as 16 pp 349– (1966)
[11] Cycle Decompositions of Kn and Kn-I, PhD thesis, Simon Fraser University, 1999.
[12] ?ajna, Discrete Math
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.