Seymour's Second Neighborhood Conjecture for Tournaments Missing a Generalized Star
نویسندگان
چکیده
منابع مشابه
The Second Neighborhood Conjecture For Oriented Graphs Missing Generalized Combs
Seymour’s Second Neighborhood Conjecture asserts that every oriented graph has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. We introduce the generalized comb, characterize them and prove that every oriented graph missing it satisfies this conjecture.
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Let D be a simple digraph without loops or digons (i.e. if (u, v) ∈ E(D), then (v, u) 6∈ E(D)). For any v ∈ V (D) let N1(v) be the set of all vertices at out-distance 1 from v and let N2(v) be the set of all vertices at out-distance 2. We provide sufficient conditions under which there must exist some v ∈ V (D) such that |N1(v)| ≤ |N2(v)|, as well as examine properties of a minimal graph which ...
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Let D be a simple digraph without loops or digons. For any v ∈ V (D) let N1(v) be the set of all nodes at out-distance 1 from v and let N2(v) be the set of all nodes at out-distance 2. We provide conditions under which there must exist some v ∈ V (D) such that |N1(v)| ≤ |N2(v)|, as well as examine extremal properties in a minimal graph which does not have such a node. We show that if one such g...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2011
ISSN: 0364-9024
DOI: 10.1002/jgt.20634