Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six

Abstract

An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors.The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ ′ a (G).We prove that χ ′ a (G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6.This gives new evidence to a conjecture proposed in [Z.