On links minimizing the tunnel number

TL;DR

This paper presents a combinatorial approach to determine the minimal tunnel number for a broad class of links, including satellite and hyperbolic types, showing it equals the number of components minus one.

Contribution

Introduces a combinatorial method to identify links with minimal tunnel number, extending to satellite and hyperbolic links.

Findings

Tunnel number equals components minus one for the studied links.

Applicable to a large class of links including satellite and hyperbolic.

Provides a combinatorial proof for minimal tunnel number.

Abstract

We show a combinatorial argument in the diagram of large class of links, including satellite and hyperbolic links, where for each of which the tunnel number is the minimum possible, the number of its components minus one.