About the second neighborhood problem in tournaments missing disjoint stars - Salman Ghazal (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 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.