Sufficient conditions for a planar graph to be list edge ΔΔ-colorable and list totally (Δ+1)(Δ+1)-colorable

Let χl′(G), χl″(G) and Δ(G)Δ(G) denote the list chromatic index, the list total chromatic number and the maximum degree of a graph GG, respectively. In this paper, we show that χl′(G)=Δ(G) and χl″(G)=Δ(G)+1 if GG is (1)a planar graph with Δ(G)≥7Δ(G)≥7 and without adjacent cycles of length at most 4; or(2)a planar graph with Δ(G)≥8Δ(G)≥8 and without cycles of length 3 adjacent to cycles of length 5. Moreover, χl′(G)≤Δ(G)+1 and χl″(G)≤Δ(G)+2 if GG is a planar graph with Δ(G)≥6Δ(G)≥6 and without cycles of length 3 adjacent to cycles of length 5.