Sufficient conditions for a planar graph to be list edge -colorable and list totally -colorable

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