Polynomial-time MWIS algorithm for S_{1,2,2}-free graphs

Establish whether the Maximum Weight Independent Set problem is solvable in polynomial time on S_{1,2,2}-free graphs.

Background

The paper surveys the complexity of Maximum Weight Independent Set on hereditary graph classes defined by forbidden induced subgraphs. It notes that claw-free graphs and fork-free graphs admit polynomial-time algorithms, while the next relevant subdivided-claw case, S_{1,2,2}, remains unresolved.

This problem concerns the smallest subdivided-claw-free graph class identified in the paper for which polynomial-time solvability of Maximum Weight Independent Set has not been confirmed.