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Article Dans Une Revue Theoretical Computer Science Année : 2017

Acyclic edge coloring through the Lovász Local Lemma

Résumé

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 ∆ has an acyclic proper edge coloring with at most ⌈3.74(∆ − 1)⌉ + 1 colors, whereas, previously, the best bound was 4(∆ − 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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Dates et versions

hal-01632338 , version 1 (22-01-2018)

Identifiants

Citer

Dimitrios M. Thilikos, Ioannis Giotis, Lefteris Kirousis, Kostas I. Psaromiligkos. Acyclic edge coloring through the Lovász Local Lemma. Theoretical Computer Science, 2017, 665, pp.40 - 50. ⟨10.1016/j.tcs.2016.12.011⟩. ⟨hal-01632338⟩
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