Strong edge-colouring of sparse planar graphs
Discrete Mathematics
2014-07-22 v3 Combinatorics
Abstract
A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree has a strong edge-colouring with at most colours. We show that colours suffice if the graph has girth 6, and colours suffice if or the girth is at least 5. In the last part of the paper, we raise some questions related to a long-standing conjecture of Vizing on proper edge-colouring of planar graphs.
Cite
@article{arxiv.1401.4568,
title = {Strong edge-colouring of sparse planar graphs},
author = {Julien Bensmail and Ararat Harutyunyan and Hervé Hocquard and Petru Valicov},
journal= {arXiv preprint arXiv:1401.4568},
year = {2014}
}