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arXiv · 1101.5721

A Coloring Algorithm for Triangle-Free Graphs

Mohammad Shoaib Jamall
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Abstract

We give a randomized algorithm that properly colors the vertices of a triangle-free graph G on n vertices using O(Δ(G)/ log Δ(G)) colors, where Δ(G) is the maximum degree of G. The algorithm takes O(n\Delta2(G)logΔ(G)) time and succeeds with high probability, provided Δ(G) is greater than log^{1+ε}n for a positive constant ε. The number of colors is best possible up to a constant factor for triangle-free graphs. As a result this gives an algorithmic proof for a sharp upper bound of the chromatic number of a triangle-free graph, the existence of which was previously established by Kim and Johansson respectively.

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Mohammad Shoaib Jamall. 2011-01-29. A Coloring Algorithm for Triangle-Free Graphs. https://arxiv.org/abs/1101.5721

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