List-edge and list-total colorings of graphs embedded on hyperbolic surfaces

In the paper, we prove that if GG is a graph embeddable on a surface of Euler characteristic ε<0ε<0 and Δ≥25−24ε+10, then χlist′(G)=Δ and χlist″(G)=Δ+1. This extends a result of Borodin, Kostochka and Woodall [O.V. Borodin, A.V. Kostochka, D.R. Woodall, List-edge and list-total colorings of multigraphs, J. Comb. Theory Series B 71 (1997) 184–204].