5 problems

Borodin's cyclic coloring conjecture. Every connected plane graph $G$ satisfies

Subdivision cyclic coloring conjecture. Every such graph $G$ satisfies

Plummer–Toft conjecture. Every simple $3$-connected plane graph $G$ satisfies

Borodin–Broersma–Glebov–van den Heuvel conjecture. Every plane graph $G$ with $\Delta^*(G)$ and $k^*$ sufficiently large has a cyclic coloring with

Let $G$ be a $3$-connected plane graph, and let $Delta^\star$ be its maximum face size. A cyclic coloring of $G$ is a vertex coloring in which any two vertices incident with the sa…