Cycle decompositions of complete graphs

Details Cycle decompositions of complete graphs Cycle decompositions of complete graphs

2012-04-17

arxiv.org/abs/1204.3709v1

Mathematics

Combinatorics

43 pages, 0 figures

Scientific paper

We show that the complete graph on n vertices can be decomposed into t cycles of specified lengths m_1,...,m_t if and only if n is odd, 3<=m_i<=n for i=1,...,t, and m_1+...+m_t=n(n-1)/2. We also show that the complete graph on n vertices can be decomposed into a perfect matching and t cycles of specified lengths m_1,...,m_t if and only if n is even, 3<=m_i<=n$ for i=1,...,t, and m_1+...+m_t=n(n-2)/2.

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