The maximum weight stable set problem in $(P_6,\mbox{bull})$-free graphs

TL;DR

This paper introduces a polynomial-time algorithm for finding maximum weight stable sets in graphs excluding specific induced subgraphs, namely $P_6$ and the bull, expanding the class of graphs where this problem is efficiently solvable.

Contribution

The paper provides the first polynomial-time algorithm for maximum weight stable sets in $(P_6, ext{bull})$-free graphs, a previously unresolved graph class.

Findings

Polynomial-time algorithm for $(P_6, ext{bull})$-free graphs

Extends tractable cases of the maximum weight stable set problem

Identifies structural properties enabling efficient computation

Abstract

We present a polynomial-time algorithm that finds a maximum weight stable set in a graph that does not contain as an induced subgraph an induced path on six vertices or a bull (the graph with vertices $a, b, c, d, e$ and edges $ab, bc, cd, be, ce$).