l-facial edge colorings of graphs
Combinatorics
2015-10-02 v1
Abstract
An l-facial edge coloring of a plane graph is a coloring of the edges such that any two edges at distance at most l on a boundary walk of some face receive distinct colors. It is conjectured that 3l + 1 colors suffice for an l-facial edge coloring of any plane graph. We prove that 7 colors suffice for a 2-facial edge coloring of any plane graph and therefore confirm the conjecture for l = 2.
Keywords
Cite
@article{arxiv.1303.4346,
title = {l-facial edge colorings of graphs},
author = {Borut Lužar and Martina Mockovčiaková and Roman Soták and Riste Škrekovski and Peter Šugerek},
journal= {arXiv preprint arXiv:1303.4346},
year = {2015}
}