Pré-Publication, Document De Travail Année : 2019

Every planar graph with Δ8 is totally (Δ+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 Δ needs at least Δ+1 colors. In the planar case, Borodin proved in 1989 that Δ+2 colors suffice when Δ is at least 9. We show that this bound also holds when Δ is 8.

Dates et versions

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

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Citer

Marthe Bonamy, Théo Pierron, Eric Sopena. Every planar graph with Δ8 is totally (Δ+2)-choosable. 2019. ⟨hal-02402914⟩

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