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The Hamilton–Waterloo problem for cycle sizes 3 and 4

✍ Scribed by Peter Danziger; Gaetano Quattrocchi; Brett Stevens

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
127 KB
Volume
17
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

The Hamilton–Waterloo problem seeks a resolvable decomposition of the complete graph K~n~, 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

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