Strong edge-colouring of sparse planar graphs [article]

Julien Bensmail, Hervé Hocquard
2014 arXiv   pre-print
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 Δ has a strong edge-colouring with at most 4Δ+4 colours. We show that 3Δ+1 colours suffice if the graph has girth 6, and 4Δ colours suffice if Δ≥ 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.
arXiv:1401.4568v3 fatcat:me52jj5svnbgbpmmg36kg73s2a