The adjacent vertex distinguishing edge choosability of planar graphs with maximum degree at least 11

Abstract

An adjacent vertex distinguishing edge coloring is a proper edge coloring such that any two adjacent vertices have distinct sets consisting of colors of their incident edges. It was conjectured that if G is a connected graph with at least 6 vertices, then χa′(G)≤Δ(G)+2. In this paper, we consider the list version of adjacent vertex distinguishing edge coloring and show that if G is a planar graph without isolated edges, then cha′(G)≤max{13,Δ(G)+2}, where cha′(G) is the adjacent vertex distinguishing edge choosability. This result implies that the above conjecture holds for planar graphs with maximum degree at least 11. Our approach is based on the Combinatorial Nullstellensatz and the discharging method.