# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

B. Liu, L. Sun , B. Wang, J.-L. Wu

Title:

The list coloring and list total coloring of planar graphs with maximum degree at least 7

Source:

Discussiones Mathematicae Graph Theory

Received: 2017-02-13, Revised: 2018-06-02, Accepted: 2018-06-21, https://doi.org/10.7151/dmgt.2160

Abstract:

A graph $G$ is edge $k$-choosable (respectively, total $k$-choosable) if, whenever we are given a list $L(x)$ of colors with $|L(x)|=k$ for each $x\in E(G)$ $(x\in E(G)\cup V(G))$, we can choose a color from $L(x)$ for each element $x$ such that no two adjacent (or incident) elements receive the same color. The list edge chromatic index $\chi'_l(G)$ (respectively, the list total chromatic number $\chi''_l(G)$) of $G$ is the smallest integer $k$ such that $G$ is edge (respectively, total) $k$-choosable. In this paper, we focus on a planar graph $G$, with maximum degree $\Delta(G)\geq 7$ and with some structural restrictions, satisfies $\chi'_l(G)=\Delta(G)$ and $\chi''_l(G)=\Delta(G)+1$.

Keywords:

planar graph, list edge coloring, list total coloring