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

• Fábio Botler ^[1] ; Phablo F. S. Moura ^[2] ; Tássio Naia ^[3]
  1. [1] Univ. Federal do Rio de Janeiro, Brasil
  2. [2] Univ. Federal de Minas Gerais, Brasil
  3. [3] Univ. de São Paulo, Brasil

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• Localización: Discrete Mathematics Days 2022 / coord. por Luis Felipe Tabera Alonso, 2022, ISBN 978-84-19024-02-2, págs. 58-63
• Idioma: inglés
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• Resumen

  • 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.