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Cayley graphs of abelian groups, circular colorings and discrete fundamental groups
Abstract
For each integer k ≥ 2, we prove that an abelian group Γ satisfies exp(Γ) ∈ {1,…,k} ∪ {2,4,…,2k} if and only if it admits no non-bipartite Cayley graph whose circular chromatic number is strictly less than 2 + 2/(k−1). This refines the algebraic characterization by Krebs and Sankar of abelian groups that admit $3$-chromatic Cayley graphs.
Related
- Frobenius Alexander quandles, knot colorings, and isogeny classes of abelian varieties over finite fields
- Abelian Cayley High-Dimensional Expanders with Polylogarithmic Degree
- Fast robbers on abelian Cayley graphs and digraphs
- Isomorphisms of abelian Cayley graphs with their natural edge-colouring
- Optimal Sparsifiers for Abelian Cayley Graphs
BibTeX
@misc{enami2026cayley,
title = {{Cayley graphs of abelian groups, circular colorings and discrete fundamental groups}},
author = {Kengo Enami and Takahiro Matsushita},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21940},
eprint = {2610.21940},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21940},
}
RIS
TY - UNPB
TI - Cayley graphs of abelian groups, circular colorings and discrete fundamental groups
AU - Kengo Enami
AU - Takahiro Matsushita
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.21940
UR - https://arxiv.org/abs/2610.21940
AB - For each integer k ≥ 2, we prove that an abelian group Γ satisfies exp(Γ) ∈ {1,…,k} ∪ {2,4,…,2k} if and only if it admits no non-bipartite Cayley graph whose circular chromatic number is strictly less than 2 + 2/(k−1). This refines the algebraic characterization by Krebs and Sankar of abelian groups that admit $3$-chromatic Cayley graphs.
ER -