Strong edge coloring of planar graphs
Combinatorics
2014-02-24 v2
Abstract
A strong edge coloring of a graph is a proper edge coloring where the edges at distance at most two receive distinct colors. It is known that every planar graph with maximum degree D has a strong edge coloring with at most 4D + 4 colors. We show that 3D + 6 colors suffice if the graph has girth 6, and 3D colors suffice if the girth is at least 7. Moreover, we show that cubic planar graphs with girth at least 6 can be strongly edge colored with at most 9 colors.
Cite
@article{arxiv.1303.4580,
title = {Strong edge coloring of planar graphs},
author = {Dávid Hudák and Borut Lužar and Roman Soták and Riste Škrekovski},
journal= {arXiv preprint arXiv:1303.4580},
year = {2014}
}