Stable sets in {ISK4,wheel}-free graphs

TL;DR

This paper presents an algorithm with polynomial time complexity for finding the maximum weight stable set in graphs that exclude both ISK4 and wheel induced subgraphs, expanding understanding of such graph classes.

Contribution

It introduces an O(|V(G)|^7)-time algorithm for maximum weight stable set in {ISK4,wheel}-free graphs, a new class with specific structural restrictions.

Findings

Algorithm efficiently computes maximum stable sets.

Defines and characterizes {ISK4,wheel}-free graphs.

Provides complexity analysis of the algorithm.

Abstract

An ISK4 in a graph G is an induced subgraph of G that is isomorphic to a subdivision of K4 (the complete graph on four vertices). A wheel is a graph that consists of a chordless cycle, together with a vertex that has at least three neighbors in the cycle. A graph is {ISK4,wheel}-free if it has no ISK4 and does not contain a wheel as an induced subgraph. We give an O(|V(G)|^7)-time algorithm to compute the maximum weight of a stable set in an input weighted {ISK4,wheel}-free graph G with non-negative integer weights.