A contribution to the second neighborhood problem

Details A contribution to the second neighborhood problem A contribution to the second neighborhood problem

2011-06-27

arxiv.org/abs/1106.5462v1

Mathematics

Combinatorics

Scientific paper

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.

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