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2010

An asymptotic solution to the cycle decomposition problem for complete graphs

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An asymptotic solution to the cycle decomposition problem for complete graphs
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 m1 + m2 + · · · mt = n 2 . 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.
Darryn E. Bryant, Daniel Horsley
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JCT
Authors Darryn E. Bryant, Daniel Horsley
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