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

Smith, Benjamin R. (2010) Decomposing complete equipartite graphs into odd square-length cycles: Number of parts odd. Journal of Combinatorial Designs, 18 6: 401-414. doi:10.1002/jcd.20268


Author Smith, Benjamin R.
Title Decomposing complete equipartite graphs into odd square-length cycles: Number of parts odd
Journal name Journal of Combinatorial Designs   Check publisher's open access policy
ISSN 1063-8539
1520-6610
Publication date 2010-11
Sub-type Article (original research)
DOI 10.1002/jcd.20268
Volume 18
Issue 6
Start page 401
End page 414
Total pages 14
Place of publication Hoboken, NJ., United States
Publisher John Wiley & Sons
Collection year 2011
Language eng
Formatted 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 λ are positive integers with n 3, λ≥ 3 and n and λ both odd, then the complete equipartite graph having n parts of size m admits a decomposition into cycles of length λ2 whenever nm ≥ λ2 and λ divides m. As a corollary, we obtain necessary and sufficient conditions for the decomposition of any complete equipartite graph into cycles of length p2, where p is prime. © 2010 Wiley Periodicals, Inc. 
Keyword Cycle decompositions
Multigraph
Multipartite graph
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 3 times in Scopus Article | Citations
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Created: Sun, 05 Dec 2010, 00:09:00 EST