Stable Sets in {ISK₄,wheel}-Free Graphs

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