List colouring triangle free planar graphs

TL;DR

This paper proves that triangle-free planar graphs with a specific list assignment are always list-colorable, extending understanding of graph coloring constraints in planar graphs.

Contribution

It establishes a new list-coloring result for triangle-free planar graphs with mixed list sizes, generalizing previous coloring theorems.

Findings

Triangle-free planar graphs are list-colorable under specified list size conditions.

The result applies to graphs with an independent set and mixed list sizes.

This extends known coloring theorems for planar graphs.

Abstract

This paper proves the following result: Assume $G$ is a triangle free planar graph, $X$ is an independent set of $G$. If $L$ is a list assignment of $G$ such that $\mid L(v)\mid = 4$ for each vertex $v \in V(G)-X$ and $\mid L(v)\mid = 3$ for each vertex $v \in X$, then $G$ is $L$-colourable.