Decomposing complete equipartite graphs into cycles of length 2p

Smith, Benjamin R. (2008) Decomposing complete equipartite graphs into cycles of length 2p. Journal of Combinatorial Designs, 16 3: 244-252. doi:10.1002/jcd.20173


Author Smith, Benjamin R.
Title Decomposing complete equipartite graphs into cycles of length 2p
Formatted title
Decomposing complete equipartite graphs into cycles of length 2p
Journal name Journal of Combinatorial Designs   Check publisher's open access policy
ISSN 1063-8539
1520-6610
Publication date 2008-05
Year available 2007
Sub-type Article (original research)
DOI 10.1002/jcd.20173
Volume 16
Issue 3
Start page 244
End page 252
Total pages 9
Place of publication Hoboken, NJ, United States
Publisher John Wiley & Sons
Language eng
Formatted abstract
It is an open problem to determine whether a complete equipartite graph Km * K̄n (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 Km * K̄n into cycles of length 2p (where p ≥ 3 is a prime) are also sufficient.
Keyword Graph decomposition
Cycle decomposition
Equipartite graph
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Article first published online: 5 NOV 2007

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Citation counts: TR Web of Science Citation Count  Cited 10 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 03 Sep 2009, 10:11:42 EST by Mr Andrew Martlew on behalf of Mathematics