Cycle decompositions V: Complete graphs into cycles of arbitrary lengths

Bryant, D., Horsley, D. and Pettersson, W. (2014) Cycle decompositions V: Complete graphs into cycles of arbitrary lengths. Proceedings of the London Mathematical Society, 108(5), pp. 1153-1192. (doi:10.1112/plms/pdt051)

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Abstract

We show that the complete graph on n vertices can be decomposed into t cycles of specified lengths m1, …, mt if and only if n is odd, 3⩽mi⩽n for i=1, …, t, and m 1 + ⋯ + m t = ( n 2 ) . We also show that the complete graph on n vertices can be decomposed into a perfect matching and t cycles of specified lengths m1, …, mt if and only if n is even, 3⩽mi⩽n for i=1, …, t, and m 1 + ⋯ + m t = ( n 2 ) − n / 2 .

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Pettersson, Dr William
Authors: Bryant, D., Horsley, D., and Pettersson, W.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Proceedings of the London Mathematical Society
Publisher:London Mathematical Society
ISSN:0024-6115
ISSN (Online):1460-244X
Published Online:16 October 2013

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