Some New Methods for Constructing 4-critical Planar Graphs

TL;DR

This paper introduces novel methods for constructing larger 4-critical planar graphs by combining smaller 4-critical graphs, advancing understanding of graph coloring properties.

Contribution

It presents new techniques for building larger 4-critical planar graphs from smaller ones, expanding the toolkit for graph theorists.

Findings

New methods for constructing 4-critical planar graphs

Enhanced understanding of graph coloring criticality

Potential applications in graph coloring problems

Abstract

A graph $G$ is said to be $k$-critical if $G$ is $k$-colorable and $G-e$ is not $k$-colorable for every edge $e$ of $G$. In this paper, we present some new methods from two or more small 4-critical graphs to construct a larger 4-critical planar graphs.