An Asymptotic Version of the Multigraph 1-Factorization Conjecture
Version of Record online: 14 MAR 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 72, Issue 1, pages 19–29, January 2013
How to Cite
Vaughan, E. R. (2013), An Asymptotic Version of the Multigraph 1-Factorization Conjecture. J. Graph Theory, 72: 19–29. doi: 10.1002/jgt.21629
- Issue online: 23 OCT 2012
- Version of Record online: 14 MAR 2012
- Manuscript Revised: 17 OCT 2011
- Manuscript Received: 1 NOV 2010
- edge-coloring, multigraph
We give a self-contained proof that for all positive integers r and all , there is an integer such that for all any regular multigraph of order 2n with multiplicity at most r and degree at least is 1-factorizable. This generalizes results of Perković and Reed (Discrete Math 165/166 (1997), 567–578) and Plantholt and Tipnis (J London Math Soc 44 (1991), 393–400).