# Colored Unlinking

## TL;DR

This paper investigates the minimal crossing changes required to unlink two-component links with linking number zero, focusing on unknotted components and providing data and insights into unlinking asymmetry.

## Contribution

It introduces new results on the minimal crossing changes for unlinking two-component links with specific constraints, including data for links up to ten crossings.

## Key findings

- Unlinking asymmetry between components
- Data for links with up to ten crossings
- Conditions for minimal crossing changes

## Abstract

In links with two components there are three different types of crossings: self-crossings in the first component, self crossings in the second component, and crossings between components. In this paper we examine the minimum number of crossing changes needed to unlink without changing the crossings between components. We restrict our attention to unlinking two component links with linking number zero and both components unknotted. We provide data for links with no more than ten crossings and general results about asymmetry of unlinking between components.