We give various reformulations of the Strong Perfect Graph Conjecture, based on a study of forced coloring procedures, uniquely colorable subgraphs and ! ? 1-cliques in minimal imperfect graphs.

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Complements or Substitutes? Task Specialization by Gender and Nativity in Spain Learning about the impact of immigration on the labor market outcomes of natives is a topic of major concern for immigrant-receiving countries. There exists an extensive literature evaluating the impact of immigration on the employment and wages of natives in the U.S. Yet, despite the significant degree of occupatio...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

Perfect graphs were defined by Claude Berge in the 1960s. They are important objects for graph theory, linear programming and combinatorial optimization. Claude Berge made a conjecture about them, that was proved by Chudnovsky, Robertson, Seymour and Thomas in 2002, and is now called the strong perfect graph theorem. This is a survey about perfect graphs, mostly focused on the strong perfect gr...

Complements or Substitutes? Task Specialization by Gender and Nativity in Spain Learning about the impact of immigration on the labor market outcomes of natives is a topic of major concern for immigrant-receiving countries. There exists an extensive literature evaluating the impact of immigration on the employment and wages of natives in the U.S. Yet, despite the significant degree of occupatio...