Cyclic coloring of plane graphs with maximum face size 16 and 17

Abstract

Plummer and Toft conjectured in 1987 that the vertices of every 3-connected plane graph with maximum face size Δ⋆ can be colored using at most Δ⋆+2 colors in such a way that no face is incident with two vertices of the same color. The conjecture has been proven for Δ⋆=3, Δ⋆=4 and Δ⋆≥18. We prove the conjecture for Δ⋆=16 and Δ⋆=17.