The black-and-white coloring problem on circle graphs

TL;DR

This paper proves that the black-and-white coloring problem can be solved efficiently on circle graphs and permutation graphs, expanding the classes of graphs where the problem is polynomial-time solvable.

Contribution

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

Findings

The problem is polynomial on permutation graphs.

The problem is polynomial on circle graphs.

This extends known results to broader graph classes.

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 two vertices x in B and y in W are adjacent. In this paper we show that the problem is polynomial when restricted to permutation graphs and, more generally, to circle graphs.