If a graph is perfect, then the independence number can be computed efficiently: Maria Chudnovsky, Gérard Cornuéjols, Xinming Liu, Paul Seymour and Kristina Vušković proved that Berge graphs can be recognized efficiently. The Strong Perfect Graph Theorem says that a graph is perfect if, and only if, it is Berge. The independence number equals the Lovasz number for perfect graphs. And it can be computed efficiently. Sage has a built-in test .is_perfect()

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