An Asymptotic Version of the Multigraph 1-Factorization Conjecture

Details An Asymptotic Version of the Multigraph 1-Factorization Conjecture An Asymptotic Version of the Multigraph 1-Factorization Conjecture

2010-10-25

arxiv.org/abs/1010.5192v1

Mathematics

Combinatorics

13 pages, 2 figures

Scientific paper

We give a self-contained proof that for all positive integers $r$ and all
$\epsilon > 0$, there is an integer $N = N(r, \epsilon)$ such that for all $n
\ge N$ any regular multigraph of order $2n$ with multiplicity at most $r$ and
degree at least $(1+\epsilon)rn$ is 1-factorizable. This generalizes results of
Perkovi{\'c} and Reed, and Plantholt and Tipnis.

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