Seymour’s Second Neighborhood Conjecture on sparse random graphs

  • Fábio Botler UFRJ
  • Phablo Moura UFMG
  • Tássio Naia USP


Seymour’s Second Neighborhood Conjecture (SNC) says that every oriented graph contains a vertex whose second neighborhood is at least as large as its first neighborhood. We prove that asymptotically almost surely (a.a.s.) every orientation of the binomial random graph G(n, p) satisfies the SNC if n4p6 → 0. We also show that if p ∈ (0, 2/3), then a.a.s. a uniformly-random orientation of G(n, p) satisfies the SNC, settling it for almost every labeled oriented graph.

Palavras-chave: binomial random graph, second neighbor conjecture, orientations


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BOTLER, Fábio; MOURA, Phablo; NAIA, Tássio. Seymour’s Second Neighborhood Conjecture on sparse random graphs. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 7. , 2022, Niterói. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2022 . p. 37-40. ISSN 2595-6116. DOI: