The Minimal Coloring Number Of Any Non-splittable $\mathbb{Z}$-colorable Link Is Four
Meiqiao Zhang, Xian’an Jin, Qingying Deng · arXiv (Cornell University) · 2017
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.