Papers › Every planar graph with Δ⩾8 is totally (Δ+2)-choosable
Every planar graph with Δ⩾8 is totally (Δ+2)-choosable
Marthe Bonamy, Théo Pierron, Éric Sopena
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections