Acyclic Edge Coloring through the Lovász Local Lemma
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by
Ioannis Giotis, Lefteris Kirousis, Kostas I. Psaromiligkos, and
Dimitrios M. Thilikos
2014
Abstract
We give a probabilistic analysis of a Moser-type algorithm for the Lovász
Local Lemma (LLL), adjusted to search for acyclic edge colorings of a graph. We
thus improve the best known upper bound to acyclic chromatic index, also
obtained by analyzing a similar algorithm, but through the entropic method
(basically counting argument). Specifically we show that a graph with maximum
degree Δ has an acyclic proper edge coloring with at most
3.74(Δ-1)+1 colors, whereas, previously, the best bound was
4(Δ-1). The main contribution of this work is that it comprises a
probabilistic analysis of a Moser-type algorithm applied to events pertaining
to dependent variables.
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