List edge and list total colorings of planar graphs without short cycles

Let G be a planar graph with maximum degree Δ(G). We use and to denote the list edge chromatic number and list total chromatic number of G, respectively. In this paper, it is proved that and if Δ(G)⩾6 and G has neither C4 nor C6, or Δ(G)⩾7 and G has neither C5 nor C6, where Ck is a cycle of length k.