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Acyclic Edge-Coloring of Planar Graphs

Basavaraju, Manu and Chandran, Sunil L and Cohen, Nathann and Havet, Frederic and Mueller, Tobias (2011) Acyclic Edge-Coloring of Planar Graphs. In: SIAM Journal on Discrete Mathematics, 25 (2). pp. 463-478.

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A proper edge-coloring with the property that every cycle contains edges of at least three distinct colors is called an acyclic edge-coloring. The acyclic chromatic index of a graph G, denoted. chi'(alpha)(G), is the minimum k such that G admits an acyclic edge-coloring with k colors. We conjecture that if G is planar and Delta(G) is large enough, then chi'(alpha) (G) = Delta (G). We settle this conjecture for planar graphs with girth at least 5. We also show that chi'(alpha) (G) <= Delta (G) + 12 for all planar G, which improves a previous result by Fiedorowicz, Haluszczak, and Narayan Inform. Process. Lett., 108 (2008), pp. 412-417].

Item Type: Journal Article
Publication: SIAM Journal on Discrete Mathematics
Publisher: Society for Industrial and Applied Mathematics
Additional Information: Copyright of this article belongs to Society for Industrial and Applied Mathematics.
Keywords: edge-coloring;planar graphs;bounded density graphs
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 18 Jul 2011 07:44
Last Modified: 18 Jul 2011 07:44
URI: http://eprints.iisc.ac.in/id/eprint/39203

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