About The Second Neighborhood Problem in Tournaments Missing Disjoint Stars

Details About The Second Neighborhood Problem in Tournaments Missing Disjoint Stars About The Second Neighborhood Problem in Tournaments Missing Disjoint Stars

2011-06-27

arxiv.org/abs/1106.5463v1

Mathematics

Combinatorics

Scientific paper

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 2 such
vertices.

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