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An Asymptotic Version of the Multigraph 1-Factorization Conjecture



We give a self-contained proof that for all positive integers r and all inline image, there is an integer inline image such that for all inline image any regular multigraph of order 2n with multiplicity at most r and degree at least inline image 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).

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