Contributions to Seymour's Second Neighborhood Conjecture

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Let D be a simple digraph without loops or digons. For any v in V(D) let N_1(v) be the set of all nodes at out-distance 1 from v and let N_2(v) be the set of all nodes at out-distance 2. We provide sufficient conditions under which there must exist some v in V(D) such that |N_1(v)| is less than or equal to |N_2(v)|, as well as examine properties of a minimal graph which does not have such a node. We show that if one such graph exists, then there exist infinitely many strongly-connected graphs having no such vertex.
9 pages, 4 figures

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Combinatorics, 05C20

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http://salesiana.dossiersoluciones.com/handle/123456789/167186

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.0946
 http://arxiv.org/abs/0808.0946

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arXiv