Acyclic Edge Coloring through the Lovász Local Lemma release_3vtdf65pqzff5hgiuilktc6veq

by Ioannis Giotis, Lefteris Kirousis, Kostas I. Psaromiligkos, and Dimitrios M. Thilikos

Released as a article .

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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Date   2014-07-23
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arXiv  1407.5374v2
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