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https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

Article in volume

Authors:

Z. Liang

Zuosong Liang

Qufu Normal University

email: liangzuosong@126.com

Title:

Total coloring of claw-free planar graphs

PDF

Source:

Discussiones Mathematicae Graph Theory 42(3) (2022) 771-777

Received: 2019-05-14 , Revised: 2020-01-19 , Accepted: 2020-01-19 , Available online: 2020-02-04 , 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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