About the second neighborhood problem in tournaments missing disjoint stars

Salman Ghazal


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.


oriented graph, out-neighborhood; second out-neighborhood; star

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DOI: http://dx.doi.org/10.5614/ejgta.2016.4.2.6


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