Edge DP-Coloring in K4-Minor Free Graphs and Planar Graphs

The edge DP-chromatic number of G, denoted by χDP′ (G), is the minimum k such that G is edge DP-k-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of K4-minor free graph G with Δ≥3 is Δ. In this paper, we prove that if G is a K4-minor free graph, then χDP′ (G) ∈Δ, Δ+1, and equality χDP′ (G) =Δ+1 holds for some K4-minor free graph G with Δ=3. Moreover, if G is a planar graph with Δ≥9 and with no intersecting triangles, then χDP′ (G) =Δ.