On the chromatic number of Latin square graphs

TL;DR

This paper investigates the chromatic number of Latin square graphs, providing exact values for circulant Latin squares, bounds for others, and computational results for squares up to order eight.

Contribution

It determines the chromatic number for circulant Latin squares and offers bounds and computational data for various classes of Latin squares.

Findings

Chromatic number of circulant Latin squares determined

Bounds established for other Latin square classes

Computational results for Latin squares up to order eight

Abstract

The chromatic number of a Latin square is the least number of partial transversals which cover its cells. This is just the chromatic number of its associated Latin square graph. Although Latin square graphs have been widely studied as strongly regular graphs, their chromatic numbers appear to be unexplored. We determine the chromatic number of a circulant Latin square, and find bounds for some other classes of Latin squares. With a computer, we find the chromatic number for all main classes of Latin squares of order at most eight.