Remarks on the second neighborhood problem

D. Fidler, R. Yuster

Research output: Contribution to journalArticlepeer-review


The second neighborhood conjecture of Seymour asserts that for any orientation G = (V, E), there exists a vertex v ∈ V so that |N +(v)| ≤|Ë/++(õ)|. The conjecture was resolved by Fisher for tournaments. In this article, we prove the second neighborhood conjecture for several additional classes of dense orientations. We also prove some approximation results, and reduce an asymptotic version of the conjecture to a finite case.

Original languageEnglish
Pages (from-to)208-220
Number of pages13
JournalJournal of Graph Theory
Issue number3
StatePublished - Jul 2007


  • Orientation
  • Second neighborhood
  • Tournament

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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