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首页> 外文期刊>Hormone molecular biology and clinical investigation. >The Second Neighbourhood for Bipartite Tournaments
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The Second Neighbourhood for Bipartite Tournaments

机译：双方的比赛的第二个街区

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摘要

Let T (X ∪ Y, A) be a bipartite tournament with partite sets X, Y and arc set A. For any vertex x ∈ X ∪Y, the second out-neighbourhood N++(x) of x is the set of all vertices with distance 2 from x. In this paper, we prove that T contains at least two vertices x such that |N++(x)| ≥ |N+(x)| unless T is in a special class ?1 of bipartite tournaments; show that T contains at least a vertex x such that |N++(x)| ≥ |N?(x)| and characterize the class ?2 of bipartite tournaments in which there exists exactly one vertex x with this property; and prove that if |X| = |Y | or |X| ≥ 4|Y |, then the bipartite tournament T contains a vertex x such that |N++(x)|+|N+(x)| ≥ 2|N?(x)|.
机译：让T (X∪Y)是一个由两部分构成的比赛深裂的集X, Y和弧答:对于任何顶点X∈X∪Y,第二out-neighbourhood N + + X (X)随着距离的所有顶点的集合2x。在本文中,我们证明了T包含在至少两个顶点x这样| N + + (x) |≥| N + (x) |除非是在一个特殊的类? 1由两部分构成的比赛;顶点x这样| N + + (x) |≥| N ? (x) |描述类? 2由两部分构成的存在一个比赛顶点x这个属性;| X Y | = | |和| |≥4 Y | |,然后由两部分构成的比赛T x,包含一个顶点

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