The black-and-white coloring problem on distance hereditary graphs and strongly chordal graphs

TL;DR

This paper investigates the computational complexity of the black-and-white coloring problem across various graph classes, providing polynomial algorithms for some and NP-completeness results for others.

Contribution

It establishes polynomial-time solutions for cographs, distance-hereditary graphs, interval graphs, and strongly chordal graphs, and proves NP-completeness for splitgraphs.

Findings

Polynomial algorithms for certain graph classes

NP-completeness on splitgraphs

Clarifies complexity landscape of the problem

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 cographs, distance-hereditary graphs, interval graphs and strongly chordal graphs. We show that the problem is NP-complete on splitgraphs.