Abstract
The problem of minimum number of choosability of graphs was first introduced by Vizing. It appears in some practical problems when concerning frequency assignment. In this paper, we study two important list coloring, list edge coloring and list total coloring. We prove that $$\chi '_{l}(G)=\varDelta $$?l?(G)=Δ and $$\chi ''_{l}(G)=\varDelta +1$$?l??(G)=Δ+1 for planar graphs with $$\varDelta \ge 8$$Δ?8 and without adjacent 4-cycles.
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