Resumen de The number of the maximal triangle-free graphs

József Balogh, Sárka Petrícková

• Paul Erdos suggested the following problem: Determine or estimate the number of maximal triangle-free graphs on n vertices. Here we show that the number of maximal triangle-free graphs is at most 2 n 2 /8+o(n 2 ) , which matches the previously known lower bound.

  Our proof uses among others the Ruzsa�Szemerédi triangle-removal lemma, and recent results on characterizing of the structure of independent sets in hypergraphs