The Hamilton-Waterloo problem for cycle sizes 3 and 4

The Hamilton–Waterloo problem seeks a resolvable decomposition of the complete graph Kn, or the complete graph minus a 1‐factor as appropriate, into cycles such that each resolution class contains only cycles of specified sizes. We completely solve the case in which the resolution classes are either...

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Bibliographic Details
Published in:Journal of combinatorial designs 2009-07, Vol.17 (4), p.342-352
Main Authors: Danziger, Peter, Quattrocchi, Gaetano, Stevens, Brett
Format: Article
Language:English
Subjects:
cycle decompositions
graph factorizations
Hamilton-Waterloo problem
resolvable graph decompositions
uniform resolutions
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Summary:The Hamilton–Waterloo problem seeks a resolvable decomposition of the complete graph Kn, or the complete graph minus a 1‐factor as appropriate, into cycles such that each resolution class contains only cycles of specified sizes. We completely solve the case in which the resolution classes are either all 3‐cycles or 4‐cycles, with a few possible exceptions when n=24 and 48. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 342–352, 2009
ISSN:1063-8539
1520-6610
DOI:10.1002/jcd.20219