Discussiones Mathematicae Graph Theory 33(4) (2013) 759-770
doi: 10.7151/dmgt.1708

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Precise upper bound for the strong edge chromatic number of sparse planar graphs

Oleg V. Borodin

Institute of Mathematics
Siberian Branch of the Russian Academy of Sciences
and
Novosibirsk State University, Novosibirsk, 630090, Russia

Anna O. Ivanova

Institute of Mathematics of
Ammosov North-Eastern Federal University
Yakutsk, 677891, Russia

Abstract

We prove that every planar graph with maximum degree Δ is strong edge (2 Δ −1)-colorable if its girth is at least 40⌊ Δ/2⌋ +1. The bound 2 Δ −1 is reached at any graph that has two adjacent vertices of degree Δ.

Keywords: planar graph, edge coloring, 2-distance coloring, strong edge-coloring

2010 Mathematics Subject Classification: 05C15.

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Received 4 November 2011
Revised 20 September 2012
Accepted 20 September 2012