DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

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

Discussiones Mathematicae Graph Theory

Article in press


Authors:

Z. Liang

Title:

Total colorings of claw-free planar graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-05-14, Revised: 2020-01-19, Accepted: 2020-01-19, https://doi.org/10.7151/dmgt.2300

Abstract:

A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. Let $\Delta(G)$ be the maximum degree of $G$. Vizing conjectured that every graph has a total $(\Delta+2)$-coloring. This Total Coloring Conjecture remains open even for planar graphs, for which the only open case is $\Delta=6$. Claw-free planar graphs have $\Delta\leq 6$. In this paper, we prove that the Total Coloring Conjecture holds for claw-free planar graphs.

Keywords:

total coloring, total coloring conjecture, planar graph, claw

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