Resumen de Seymour’s second neighborhood conjecture in arbitrary orientationsof a random graph

Fábio Botler, Phablo F. S. Moura, Tássio Naia

• A famous conjecture of Seymour, known as Second Neighborhood Conjecture (SNC),says that every orientation of a graph contains a vertex whose second neighborhood is aslarge as its first neighborhood. We confirm this conjecture for arbitrary orientations of therandom graph G(n, p), in a wide range of p. More precisely, we prove that the SNC holdsasymptotically almost surely for every orientation of G(n, p), for all p = p(n) such thatlim supn→∞ p < 1/4.