Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs - Borodin Oleg V.; Ivanova Anna O. (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+1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.