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Strong chromatic index of planar graphs with large girth

Gerard Jennhwa Chang 1 Mickaël Montassier 2 Arnaud Pêcher 3, 4 André Raspaud 4
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Let Δ ≥ 4 be an integer. In this note, we prove that every planar graph with maximum degree Δ and girth at least 1 Δ+46 is strong (2Δ−1)-edgecolorable, that is best possible (in terms of number of colors) as soon as G contains two adjacent vertices of degree Δ. This improves [6] when Δ ≥ 6.
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Submitted on : Thursday, December 19, 2013 - 2:22:28 PM
Last modification on : Thursday, July 4, 2019 - 3:56:51 PM

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Gerard Jennhwa Chang, Mickaël Montassier, Arnaud Pêcher, André Raspaud. Strong chromatic index of planar graphs with large girth. Discussiones Mathematicae Graph Theory, University of Zielona Góra, 2014, 34 (4), pp.723-733. ⟨10.7151/dmgt.1763⟩. ⟨hal-00920932⟩



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