Strong edge-colorings of planar graphs with small girth

作者：

Highlights：

• Present some structural properties of planar graphs with small maximum degree.

• Define semi-poor boundary vertex (3s-boundary vertex) of a face f according to the number of its 2-neighbors on the face f, and therefore simplifies the discharging rules and calculation for final charges of faces.

• Show the bound 3D-2, 3D-3 for the strong chromatic indices of planar graphs with maximum degree at least 4, 5, and extend two previous results.

摘要

•Present some structural properties of planar graphs with small maximum degree.•Define semi-poor boundary vertex (3s-boundary vertex) of a face f according to the number of its 2-neighbors on the face f, and therefore simplifies the discharging rules and calculation for final charges of faces.•Show the bound 3D-2, 3D-3 for the strong chromatic indices of planar graphs with maximum degree at least 4, 5, and extend two previous results.

论文关键词：Strong edge-coloring,Planar graph,Discharging method

论文评审过程：Received 16 July 2020, Revised 3 October 2020, Accepted 8 November 2020, Available online 4 December 2020, Version of Record 4 December 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125796