A simple proof for the chromatic number of cyclic Latin squares of even order

TL;DR

This paper presents a straightforward coloring method for cyclic Latin squares of even order, proving their chromatic number is 2n+2 with a simple, graphically supported approach.

Contribution

It introduces a simple, graphical coloring technique for cyclic Latin squares of even order, providing an easier proof of their chromatic number.

Findings

Chromatic number of cyclic Latin squares of order 2n is 2n+2

Introduces a simple coloring method supported by graphical presentation

Simplifies previous lengthy proofs

Abstract

The chromatic number of a cyclic Latin square of order 2n is 2n+2. The available proof for this statement includes a coloring that is rather lengthy. Here, we introduce a coloring of cyclic Latin square of even order 2n (the Latin square of a cyclic group's Cayley table) with 2n+2 colors using a simple method supported by a graphical presentation.