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Pré-Publication, Document De Travail Année : 2019

Every planar graph with $\Delta\geqslant 8$ is totally $(\Delta+2)$-choosable

Résumé

Total coloring is a variant of edge coloring where both vertices and edges are to be colored. A graph is totally $k$-choosable if for any list assignment of $k$ colors to each vertex and each edge, we can extract a proper total coloring. In this setting, a graph of maximum degree $\Delta$ needs at least $\Delta+1$ colors. In the planar case, Borodin proved in 1989 that $\Delta+2$ colors suffice when $\Delta$ is at least 9. We show that this bound also holds when $\Delta$ is $8$.

Dates et versions

hal-02402914 , version 1 (10-12-2019)

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Marthe Bonamy, Théo Pierron, Eric Sopena. Every planar graph with $\Delta\geqslant 8$ is totally $(\Delta+2)$-choosable. 2019. ⟨hal-02402914⟩
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