The black-and-white coloring problem on permutation graphs

TL;DR

This paper proves that the black-and-white coloring problem can be solved efficiently in polynomial time when applied to permutation graphs, expanding understanding of graph coloring complexities.

Contribution

The paper establishes the polynomial-time solvability of the black-and-white coloring problem specifically for permutation graphs.

Findings

The problem is polynomial-time solvable on permutation graphs.

Provides a new complexity classification for the problem on a specific graph class.

Enhances understanding of coloring problems in permutation graphs.

Abstract

Given a graph G and integers b and w. The black-and-white coloring problem asks if there exist disjoint sets of vertices B and W with |B|=b and |W|=w such that no vertex in B is adjacent to any vertex in W. In this paper we show that the problem is polynomial when restricted to permutation graphs.