English

A contribution to the second neighborhood problem

Combinatorics 2015-09-08 v1

Abstract

Seymour's Second Neighborhood Conjecture asserts that every digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. It is proved for tournaments, tournaments missing a matching and tournaments missing a generalized star. We prove this conjecture for classes of digraphs whose missing graph is a comb, a complete graph minus 2 independent edges, or a complete graph minus the edges of a cycle of length 5.

Keywords

Cite

@article{arxiv.1106.5462,
  title  = {A contribution to the second neighborhood problem},
  author = {Salman Ghazal},
  journal= {arXiv preprint arXiv:1106.5462},
  year   = {2015}
}
R2 v1 2026-06-21T18:28:13.775Z