The minimum number of Dehn $\mathbb Z$-colors of any nonsplittable $\mathbb Z$-colorable link is three

Eri Matsudo; Kanako Oshiro

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arXiv · 2608.19559

The minimum number of Dehn $\mathbb Z$-colors of any nonsplittable $\mathbb Z$-colorable link is three

Eri Matsudo·Kanako Oshiro

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Abstract

Our previous papers [8, 9] are the first and second to discuss minimum numbers of ``region'' colors, while minimum numbers of arc colors such as Fox colors are well-studied. As the third installment, in this paper, we investigate the minimum number of Dehn $\mathbb{Z}$-colors. In particular, we show that the minimum number of Dehn $\mathbb{Z}$-colors of a nonsplittable $\mathbb{Z}$-colorable link is three.

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Eri Matsudo, Kanako Oshiro. 2026-08-20. The minimum number of Dehn $\mathbb Z$-colors of any nonsplittable $\mathbb Z$-colorable link is three. https://arxiv.org/abs/2608.19559

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