The $N_+$-Perfect Graph Conjecture

Let $G$ be a graph. Its stable set polytope is denoted by ${\rm STAB}(G)$, and $G$ is $N_+$-perfect when $N_+(G)={\rm STAB}(G)$. An inequality has near-bipartite support when its support graph is near-bipartite.

$N_+$-Perfect Graph Conjecture. The stable set polytope of every $N_+$-perfect graph can be described by facet-defining inequalities with near-bipartite support.

This conjecture seeks a characterization of $N_+$-perfect graphs analogous to the characterization of perfect graphs by their stable set polytopes. The paper reformulates it in terms of joined a-perfect graphs, but does not provide evidence of a resolution.