Rosalind A. Hoyte
Published 2017-01-19Version 1
Bryant, Horsley, Maenhaut and Smith recently gave necessary and sufficient conditions for when the complete multigraph can be decomposed into cycles of specified lengths $m_1,m_2,\ldots,m_\tau$. In this paper we characterise exactly when there exists a packing of the complete multigraph with cycles of specified lengths $m_1,m_2,\ldots,m_\tau$. While cycle decompositions can give rise to packings by removing cycles from the decomposition, in general it is not known when there exists a packing of the complete multigraph with cycles of various specified lengths.
Comments: 9 pages, 0 figures
Decompositions of complete multigraphs into cycles of varying lengths
$m$-Cycle Packings of $(λ+μ)K_{v+u}-λK_v$: $m$ even
Indecomposable $1$-factorizations of the complete multigraph $λ K_{2n}$ for every $λ\leq 2n$
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