Colouring the Square of the Cartesian Product of Trees

TL;DR

This paper establishes bounds on the chromatic number of the square of the Cartesian product of trees, providing exact values when each tree has an even maximum degree.

Contribution

It offers new bounds on the chromatic number for the square of Cartesian products of trees, with exact results for trees with even maximum degree.

Findings

Upper and lower bounds on the chromatic number are proven.

Bounds are tight when each tree has even maximum degree.

Provides a complete characterization in specific cases.

Abstract

We prove upper and lower bounds on the chromatic number of the square of the cartesian product of trees. The bounds are equal if each tree has even maximum degree.