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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