Every planar graph with Δ ${\rm{\Delta }}$ ⩾ 8 is totally (Δ+2) $({\rm{\Delta }}+2)$‐choosable - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Graph Theory Année : 2023

Every planar graph with Δ ${\rm{\Delta }}$ ⩾ 8 is totally (Δ+2) $({\rm{\Delta }}+2)$‐choosable

Résumé

Total coloring is a variant of edge coloring where both vertices and edges are to be colored. A graph is totally‐choosable if for any list assignment of colors to each vertex and each edge, we can extract a proper total coloring. In this setting, a graph of maximum degree needs at least colors. In the planar case, Borodin proved in 1989 that colors suffice when is at least 9. We show that this bound also holds when is 8.
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hal-04587510 , version 1 (24-05-2024)

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Marthe Bonamy, Théo Pierron, Éric Sopena. Every planar graph with Δ ${\rm{\Delta }}$ ⩾ 8 is totally (Δ+2) $({\rm{\Delta }}+2)$‐choosable. Journal of Graph Theory, 2023, 104 (1), pp.17-86. ⟨10.1002/jgt.22949⟩. ⟨hal-04587510⟩
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