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

TL;DR

This paper proves that the minimal coloring number for any non-splittable $b{Z}$-colorable link is exactly four, confirming a precise invariant value for this class of links.

Contribution

It establishes that the minimal coloring number for all non-splittable $b{Z}$-colorable links is exactly four, resolving a previously known lower bound.

Findings

The minimal coloring number of non-splittable $b{Z}$-colorable links is exactly four.

The result confirms the lower bound as the exact value for this class of links.

Provides a complete characterization of the minimal coloring number for these links.

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.