Strong Chromatic Index Of Planar Graphs With Large Girth

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.

Keywords

• planar graphs
• edge coloring
• 2-distance coloring
• strong edgecoloring.