%0 Journal Article
%T Strong edge-colouring of sparse planar graphs
%A Julien Bensmail
%A Ararat Harutyunyan
%A Herv¨¦ Hocquard
%A Petru Valicov
%J Computer Science
%D 2014
%I arXiv
%X 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 $\Delta$ has a strong edge-colouring with at most $4\Delta+4$ colours. We show that $3\Delta+1$ colours suffice if the graph has girth 6, and $4\Delta$ colours suffice if $\Delta\geq 7$ 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.
%U http://arxiv.org/abs/1401.4568v3