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An asymptotic solution to the cycle decomposition problem for complete graphs
Authors:Darryn Bryant
Institution:a The University of Queensland, Department of Mathematics, Qld 4072, Australia
b Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7
Abstract:Let m1,m2,…,mt be a list of integers. It is shown that there exists an integer N such that for all n?N, the complete graph of order n can be decomposed into edge-disjoint cycles of lengths m1,m2,…,mt if and only if n is odd, 3?mi?n for i=1,2,…,t, and View the MathML source. In 1981, Alspach conjectured that this result holds for all n, and that a corresponding result also holds for decompositions of complete graphs of even order into cycles and a perfect matching.
Keywords:Cycle decompositions  Graph decompositions
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