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 Lambda* can be colored using at most Lambda* + 2 colors in such a way that no face is incident with two vertices of the same color. The conjecture has been proven for Lambda* = 3, Lambda* = 4 and Lambda* >= 18.

We prove the conjecture for Lambda* = 16 and Lambda* = 17. (c) 2020 Elsevier Ltd. All rights reserved.

Keywords

• facial colorings
• conjecture
• plummer
• map