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

TL;DR

This paper investigates the list (d,1)-total labelling of graphs embedded in surfaces, establishing an upper bound on the (d,1)-total choosability for graphs with large maximum degree.

Contribution

It extends the concept of (d,1)-total labelling to the list version for embedded graphs and provides an upper bound on the choosability based on maximum degree.

Findings

Proves an upper bound of Δ(G)+2d for (d,1)-total choosability.

Applies to graphs embedded in surfaces with large maximum degree.

Extends previous labelling results to the list setting.

Abstract

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 $\epsilon$ whose maximum degree $\Delta(G)$ is sufficiently large. We prove that the (d,1)-total choosability $C_{d,1}^T(G)$ of $G$ is at most $\Delta(G)+2d$.