Strong edge-colouring of sparse planar graphs
  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. 
Julien Bensmail (LaBRI), Ararat Harutyunyan (MI), Herv\'e Hocquard   (LaBRI), Petru Valicov (LIP)
cs.DM math.CO