A note on -colorings of graphs.

Sheng, Jian-Ting; Liu, Gui-Zhen

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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.