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Decomposing complete equipartite graphs into odd square-length cycles: Number of parts even

✍ Scribed by Benjamin R. Smith; Nicholas Cavenagh


Book ID
113567609
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
268 KB
Volume
312
Category
Article
ISSN
0012-365X

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Decomposing complete equipartite graphs
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## Abstract In this article, we introduce a new technique for obtaining cycle decompositions of complete equipartite graphs from cycle decompositions of related multigraphs. We use this technique to prove that if __n__, __m__ and Ξ» are positive integers with __n__ β‰₯ 3, Ξ»β‰₯ 3 and __n__ and Ξ» both odd

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We prove that any complete multipartite graph with parts of even size can be decomposed into closed trails with prescribed even lengths.