• Corpus ID: 231922057

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

@article{Kreher2020ASP,
  title={A simple proof for the chromatic number of cyclic Latin squares of even order},
  author={Donald L. Kreher},
  journal={Bull. ICA},
  year={2020},
  volume={89},
  pages={41-45}
}
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 squares of even order 2n (the Latin square graph of a cyclic group’s Cayley table) with 2n+2 colors using a simple method supported by a graphical presentation. 

Figures from this paper

References

SHOWING 1-4 OF 4 REFERENCES
On the chromatic index of Latin squares
TLDR
The chromatic index of the cyclic Latin square is studied, suggesting a generalization of Ryser’s conjecture (that every Latin square of odd order contains a transversal) and the best possible bounds are obtained.
The Chromatic Number of Finite Group Cayley Tables
TLDR
An upper bound for the chromatic number of Cayley tables of arbitrary finite groups is given, which improves the best-known general upper bound from $2|G|$ to $\frac{3}{2} |G|$, while yielding an even stronger result in infinitely many cases.
Mortezaeefar, On the chromatic number of Latin square graphs, Discrete Math
  • 2016