Maximum Weight Stable Set in ($P_7$, bull)-free graphs and ($S_{1,2,3}$, bull)-free graphs

TL;DR

This paper presents polynomial-time algorithms for finding maximum weight stable sets in graphs excluding certain induced subgraphs, specifically ($P_7$, bull) and ($S_{1,2,3}$, bull), expanding the class of graphs with efficient solutions.

Contribution

It introduces new polynomial algorithms for maximum weight stable sets in ($P_7$, bull)-free and ($S_{1,2,3}$, bull)-free graphs, broadening the scope of efficiently solvable graph classes.

Findings

Polynomial algorithm for ($P_7$, bull)-free graphs

Polynomial algorithm for ($S_{1,2,3}$, bull)-free graphs

Extends known classes with efficient maximum weight stable set solutions

Abstract

We give a polynomial time algorithm that finds the maximum weight stable set in a graph that does not contain an induced path on seven vertices or a bull (the graph with vertices $a$, $b$, $c$, $d$, $e$ and edges $ab$, $bc$, $cd$, $be$, $ce$). With the same arguments with also give a polynomial algorithm for any graph that does not contain $S_{1,2,3}$ or a bull.