A contribution to the second neighborhood problem

Abstract

Seymour's Second Neighborhood Conjecture asserts that every digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. It is proved for tournaments, tournaments missing a matching and tournaments missing a generalized star. We prove this conjecture for classes of digraphs whose missing graph is a comb, a complete graph minus 2 independent edges, or a complete graph minus the edges of a cycle of length 5.

References in corpus (1)

• Seymour's second neighborhood conjecture for tournaments missing a generalized star

Cited by in corpus (3)

• A Remark on the Second Neighborhood Problem
• The Second Neighborhood Conjecture for Oriented Graphs Missing $\{C_4,\overline{C_4},S_3,$ chair and co-chair$\}$-Free Graph
• The Second Neighborhood Conjecture for Oriented Graphs Missing Combs