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Sum-perfect graphs

Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph $G$ to be sum-perfect if for every induced subgraph $H$ of $G$, $α(H) + ω(H) \geq |V(H)|$. (Here $α$ and $ω$ denote the stability number and clique number, respectively.) We give a set of $27$ graphs and we prove that a graph $G$ is sum-perfect if and only if $G$ does not contain any of the graphs in the set as an induced subgraph.