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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Salman Ghazal
Department of Mathematics Faculty of Sciences I, Lebanese University, Lebanon, and Institute Camille Jordan Département de Mathématiques, Université Claude Bernard Lyon 1, France.
Electrical & Electronics Engineering

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About the second neighborhood problem in tournaments missing disjoint stars Salman Ghazal
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2016.4.2.6

Abstract

Let $D$ be a digraph without digons. Seymour's second neighborhood conjecture states that $D$ has a vertex $v$ such that $d^+(v) \leq d^{++}(v)$. Under some conditions, we prove this conjecture for digraphs missing $n$ disjoint stars. Weaker conditions are required when $n = 2$ or $3$. In some cases we exhibit two such vertices.
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