# New algorithms for the Minimum Coloring Cut Problem

## TL;DR

This paper introduces two Variable Neighborhood Search algorithms to solve the Minimum Coloring Cut Problem, effectively finding all known optimal solutions and advancing solution methods for this graph problem.

## Contribution

The paper presents novel VNS-based algorithms that successfully identify all optimal solutions for the Minimum Coloring Cut Problem, improving solution techniques.

## Key findings

- Algorithms find all known optimal solutions.
- VNS approaches outperform previous methods.
- Effective in solving complex graph instances.

## Abstract

The Minimum Coloring Cut Problem is defined as follows: given a connected graph G with colored edges, find an edge cut E' of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the edges in E' is minimum. In this work, we present two approaches based on Variable Neighborhood Search to solve this problem. Our algorithms are able to find all the optimum solutions described in the literature.