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.
Categories: math.GT math.AT