Cycle decompositions of complete multigraphs

Darryn Bryant; Daniel Horsley; Barbara Maenhaut; Benjamin Smith

doi:10.1002/jcd.20263

Cycle decompositions of complete multigraphs

Darryn Bryant, Daniel Horsley, Barbara Maenhaut, Benjamin Smith

Research output: Contribution to journal › Article › Research › peer-review

29 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 language	English
Pages (from-to)	42 - 69
Number of pages	28
Journal	Journal of Combinatorial Designs
Volume	19
Issue number	1
DOIs	https://doi.org/10.1002/jcd.20263
Publication status	Published - 2011
Externally published	Yes

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10.1002/jcd.20263

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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",

author = "Darryn Bryant and Daniel Horsley and Barbara Maenhaut and Benjamin Smith",

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AU - Horsley, Daniel

AU - Maenhaut, Barbara

AU - Smith, Benjamin

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AB - 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

UR - http://www.aarms.math.ca/paper/cycle-decompositions-of-complete-multigraphs.pdf

U2 - 10.1002/jcd.20263

DO - 10.1002/jcd.20263

M3 - Article

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VL - 19

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EP - 69

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 1

ER -

Cycle decompositions of complete multigraphs

Abstract

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