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Decomposing complete equipartite graphs into cycles of length 2p

✍ Scribed by Benjamin R. Smith

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 161 KB
Volume: 16
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20173

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✦ Synopsis

Abstract

It is an open problem to determine whether a complete equipartite graph $K_m*{\overline{K}}_n$ (having m parts of size n) admits a decomposition into cycles of arbitrary fixed length $k$ whenever m, n, and k satisfy the obvious necessary conditions for the existence of such a decomposition. Recently, Manikandan and Paulraja [6] have shown the necessary conditions are indeed sufficient for a decomposition into cycles of length p where $p>5$ is a prime. The case $p=3$ was settled by Hanani [4] and the case $p=5$ was settled by Billington et al. [2]. Here, we extend this result and show that the necessary conditions for the decomposition of $K_m*{\overline{K}}_n$ into cycles of length $2p$ (where $p\ge 3$ is a prime) are also sufficient. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 244–252, 2008

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