Total coloring of claw-free planar graphs | Zendy

Zuosong Liang | Zendy

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Total coloring of claw-free planar graphs

Author(s) -

Zuosong Liang

Publication year - 2020

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.2300

Subject(s) - mathematics , claw , combinatorics , planar graph , edge coloring , planar , graph , computer science , line graph , biology , computer graphics (images) , ecology , graph power

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 ∆(G) be the maximum degree of G. Vizing conjectured that every graph has a total (∆ + 2)-coloring. This Total Coloring Conjecture remains open even for planar graphs, for which the only open case is ∆ = 6. Claw-free planar graphs have ∆ ≤ 6. In this paper, we prove that the Total Coloring Conjecture holds for claw-free planar graphs.

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