Cycle decompositions of complete multigraphs

Darryn Bryant, Daniel Horsley, Barbara Maenhaut, Benjamin Smith

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23 Citations (Scopus)

Abstract

It is shown that the obvious necessary conditions for the existence of a decomposition of the complete multigraph with n vertices and with lambda edges joining each pair of distinct vertices into m-cycles, or into m-cycles and a perfect matching, are also sufficient. This result follows as an easy consequence of more general results which are obtained on decompositions of complete multigraphs into cycles of varying lengths
Original languageEnglish
Pages (from-to)42 - 69
Number of pages28
JournalJournal of Combinatorial Designs
Volume19
Issue number1
DOIs
Publication statusPublished - 2011
Externally publishedYes

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