The Hamilton–Waterloo problem for cycle sizes 3 and 4 |
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| Authors: | Peter Danziger Gaetano Quattrocchi Brett Stevens |
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| Institution: | 1. Department of Mathematics, Ryerson University, Toronto, Ont., Canada, M5B 2K3;2. Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy;3. School of Mathematics and Statistics, Carleton University, Ottawa, Ont., Canada, K1S 5B6 |
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| Abstract: | 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 |
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| Keywords: | Hamilton– Waterloo problem resolvable graph decompositions uniform resolutions cycle decompositions graph factorizations |
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