Adjacent vertex-distinguishing edge colorings of K4K4-minor free graphs

The adjacent vertex-distinguishing chromatic index χa′(G) of a graph GG is the smallest integer kk for which GG admits a proper edge kk-coloring such that any pair of adjacent vertices are incident to distinct sets of colors.In this paper, we prove that if GG is a K4K4-minor free graph, without isolated edges, and with maximum degree Δ≥4Δ≥4, then Δ≤χa′(G)≤Δ+1; when Δ≥5Δ≥5, χa′(G)=Δ if and only if GG contains no adjacent vertices of maximum degree.