Cyclic colorings of plane graphs with independent faces

TL;DR

This paper proves that plane graphs with disjoint large faces can be cyclically colored with a number of colors equal to the maximum face size plus one, extending coloring theory for planar graphs.

Contribution

It establishes a new upper bound for cyclic colorings of plane graphs with disjoint large faces, generalizing previous results in graph coloring.

Findings

Cyclic coloring with D+1 colors for graphs with disjoint faces of size four or more

Extension of coloring bounds to a broader class of plane graphs

Improved understanding of face-disjoint face coloring constraints

Abstract

Let G be a plane graph with maximum face size D. If all faces of G with size four or more are vertex disjoint, then G has a cyclic coloring with D+1 colors, i.e., a coloring such that all vertices incident with the same face receive distinct colors.