# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

L. Hu, L. Sun, J.-L. Wu

Title:

List coloring of planar graphs without 6-cycles with two chords

Source:

Discussiones Mathematicae Graph Theory

Received: 2017-05-22, Revised: 2018-09-10, Accepted: 2018-09-10, https://doi.org/10.7151/dmgt.2183

Abstract:

A graph $G$ is edge-$L$-colorable if for a given edge assignment $L=\{L(e):e\in E(G)\}$, there exists a proper edge-coloring $\varphi$ of $G$ such that $\varphi(e)\in L(e)$ for all $e\in E(G)$. If $G$ is edge-$L$-colorable for every edge assignment $L$ such that $|L(e)|\geq k$ for all $e\in E(G)$, then $G$ is said to be edge-$k$-choosable. In this paper, we prove that if $G$ is a planar graph without $6$-cycles with two chords, then $G$ is edge-$k$-choosable, where $k=\max\{7,\Delta(G)+1\}$, and is edge-$t$-choosable, where $t=\max\{9,\Delta(G)\}$.

Keywords:

planar graph, edge choosable, list edge chromatic number, chord