List (d,1)-total labelling of graphs embedded in surfaces

The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we consider the list version of (d,1)-total labelling of graphs. Let G be a graph embedded in a surface with Euler characteristic $ε$ whose maximum degree $Δ(G)$ is sufficiently large. We prove that the (d,1)-total choosability $C_{d,1}^T(G)$ of $G$ is at most $Δ(G)+2d$.

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