• 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. 
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References

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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.
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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.
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