Excluding 4-wheels

TL;DR

This paper proves that graphs excluding a 4-wheel subgraph are 4-colorable and explores their structural properties, contributing to graph coloring theory by identifying constraints that guarantee a bounded chromatic number.

Contribution

It introduces the class of 4-wheel-free graphs, proves their 4-colorability, and characterizes their structural properties, advancing understanding of graph colorings under specific subgraph exclusions.

Findings

4-wheel-free graphs are 4-colorable

Structural properties of 4-wheel-free graphs are characterized

Provides conditions for graph colorability based on subgraph exclusion

Abstract

A 4-wheel is a graph formed by a cycle C and a vertex not in C that has at least four neighbors in C. We prove that a graph G that does not contain a 4-wheel as a subgraph is 4-colorable and we describe some structural properties of such a graph.