Geodesic
Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 4, pp. 759-770

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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 edgecoloring 
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     title = {Precise {Upper} {Bound} for the {Strong} {Edge} {Chromatic} {Number} of {Sparse} {Planar} {Graphs}},
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Borodin, Oleg V.; Ivanova, Anna O. Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 4, pp. 759-770. http://geodesic.mathdoc.fr/item/DMGT_2013_33_4_a10/