On Colorings of Squares of Outerplanar Graphs

TL;DR

This paper investigates the coloring properties of the square of outerplanar graphs, establishing optimal bounds for various coloring parameters based on maximum degree, and classifies specific cases for chordal outerplanar graphs.

Contribution

It provides the first comprehensive bounds for the chromatic number, clique number, and choosability of the square of outerplanar graphs as functions of maximum degree.

Findings

Optimal bounds for inductiveness, chromatic number, and clique number of G^2.

Exact classification of graphs with parameters exceeding minimum in chordal outerplanar graphs.

Bounds on list-chromatic number for Δ ≥ 7.

Abstract

We study vertex colorings of the square $G^2$ of an outerplanar graph $G$. We find the optimal bound of the inductiveness, chromatic number and the clique number of $G^2$ as a function of the maximum degree $\Delta$ of $G$ for all $\Delta\in \nats$. As a bonus, we obtain the optimal bound of the choosability (or the list-chromatic number) of $G^2$ when $\Delta \geq 7$. In the case of chordal outerplanar graphs, we classify exactly which graphs have parameters exceeding the absolute minimum.