Almost resolvable minimum coverings of complete graphs with 4-cycles

Billington, Elizabeth J., Hoffman, D.G., Lindner, C. C. and Meszka, Mariusz (2011) Almost resolvable minimum coverings of complete graphs with 4-cycles. Australasian Journal of Combinatorics, 50 73-85.

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Author Billington, Elizabeth J.
Hoffman, D.G.
Lindner, C. C.
Meszka, Mariusz
Title Almost resolvable minimum coverings of complete graphs with 4-cycles
Journal name Australasian Journal of Combinatorics   Check publisher's open access policy
ISSN 1034-4942
Publication date 2011-06-01
Sub-type Article (original research)
Open Access Status Not yet assessed
Volume 50
Start page 73
End page 85
Total pages 13
Place of publication Department of Mathematics, The University of Queensland, QLD, Australia
Publisher Centre for Discrete Mathematics & Computing
Language eng
Formatted abstract
If the complete graph Kn has vertex set X, a minimum covering of Kn with 4-cycles, (X,C, P), is a partition of the edges of KnP into a collection C of 4-cycles, where P is a subgraph of λKn and the number of edges in P is as small as possible. An almost parallel class of a minimum covering of Kn with 4-cycles is a largest possible collection of vertex disjoint 4-cycles (so with ⌊n/4⌋ 4-cycles in it).
     In this paper, for all orders n, except order 9 which does not exist, we exhibit a minimum covering of Kn with 4-cycles so that the 4-cycles in the covering are resolvable into almost parallel classes, with any remaining 4-cycles being vertex disjoint.
     We also complete the missing examples of order 23 for the same problem with almost resolvable maximum packings with 4-cycles, and orders 41 and 57 in the case of an exact decomposition into 4-cycles, partitioned into almost parallel classes.
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 2012 Collection
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Citation counts: TR Web of Science Citation Count  Cited 4 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 5 times in Scopus Article | Citations
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Created: Tue, 20 Sep 2011, 21:54:00 EST by Dr Elizabeth Billington on behalf of Mathematics