## Abstract

Let D be a simple digraph without loops or digons. For any v∈V(D)

, the first out-neighborhood N +(v) is the set of all vertices with out-distance 1 from v and the second neighborhood N ++(v) of v is the set of all vertices with out-distance 2 from v. We show that every simple digraph without loops or digons contains a vertex v such that |N++(v)|≥γ|N+(v)|, where γ = 0.657298... is the unique real root of the equation 2x 3 + x 2 -1 = 0.

, the first out-neighborhood N +(v) is the set of all vertices with out-distance 1 from v and the second neighborhood N ++(v) of v is the set of all vertices with out-distance 2 from v. We show that every simple digraph without loops or digons contains a vertex v such that |N++(v)|≥γ|N+(v)|, where γ = 0.657298... is the unique real root of the equation 2x 3 + x 2 -1 = 0.

Original language | English |
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Pages (from-to) | 15–20 |

Journal | Annals of Combinatorics |

Volume | 7. |

DOIs | |

State | Published - 2003 |