The Minimal Coloring Number Of Any Non-splittable $\mathbb{Z}$-colorable Link Is Four

Meiqiao Zhang; Xian'an Jin; Qingying Deng

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arXiv · 1706.08837

The Minimal Coloring Number Of Any Non-splittable $\mathbb{Z}$-colorable Link Is Four

Meiqiao Zhang·Xian'an Jin·Qingying Deng

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Abstract

K. Ichihara and E. Matsudo introduced the notions of $\mathbb{Z}$-colorable links and the minimal coloring number for $\mathbb{Z}$-colorable links, which is one of invariants for links. They proved that the lower bound of minimal coloring number of a non-splittable $\mathbb{Z}$-colorable link is 4. In this paper, we show the minimal coloring number of any non-splittable $\mathbb{Z}$-colorable link is exactly 4.

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Meiqiao Zhang, Xian'an Jin, Qingying Deng. 2017-06-11. The Minimal Coloring Number Of Any Non-splittable $\mathbb{Z}$-colorable Link Is Four. https://arxiv.org/abs/1706.08837

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