About the second neighborhood problem in tournaments missing disjoint stars - Salman Ghazal (Electronic Journal of Graph Theory and Applications (EJGTA), 2016)
Let $D$ be a digraph without digons. Seymour's second neighborhood conjecture states that $D$ has a vertex $v$ such that $d^+(v) ≤ d^{++}(v)$. 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.