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arXiv · 2610.21940

Cayley graphs of abelian groups, circular colorings and discrete fundamental groups

Kengo Enami·Takahiro Matsushita
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Abstract

For each integer $k \ge 2$, we prove that an abelian group $Γ$ satisfies $\exp(Γ) \in \{1,\dots,k\} \cup \{2,4,\dots,2k\}$ if and only if it admits no non-bipartite Cayley graph whose circular chromatic number is strictly less than $2 + \frac{2}{k-1}$. This refines the algebraic characterization by Krebs and Sankar of abelian groups that admit $3$-chromatic Cayley graphs.

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Kengo Enami, Takahiro Matsushita. 2026-10-15. Cayley graphs of abelian groups, circular colorings and discrete fundamental groups. https://arxiv.org/abs/2610.21940

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