Precise upper bound for the strong edge chromatic number of sparse planar graphs
Oleg Veniaminovich Borodin, Anna O. Ivanova · Discussiones Mathematicae Graph Theory · 2013
We prove that every planar graph with maximum degree ∆ is strong edge (2∆ -1)-colorable if its girth is at least 40⌊ ∆ 2 ⌋ + 1.The bound 2∆ -1 is reached at any graph that has two adjacent vertices of degree ∆.