Strong edge-coloring of planar graphs

A strong edge-coloring of a graph is a proper edge-coloring where the edges at distance at most 2 receive distinct colors. It is known that every planar graph G has a strong edge-coloring with at most 4 Δ ( G ) + 4 colors. We show that 3 Δ ( G ) + 5 colors suffice if G has girth 6 , and 3 Δ ( G ) colors suffice if its girth is at least 7 . Moreover, we show that cubic planar graphs with girth at least 6 can be strongly edge-colored with at most nine colors.