The number of the maximal triangle-free graphs

• Autores: József Balogh, Sárka Petrícková
• Localización: Bulletin of the London Mathematical Society, ISSN 0024-6093, Vol. 46, Nº 5, 2014, págs. 1003-1006
• Idioma: inglés
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• Resumen

  • 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