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 )|.
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机译：令T（X∪Y，A）为二部比赛，其中有部分集X，Y和弧线集合A。对于任何顶点x∈X∪Y，x的第二个邻域N〜（++）（x）是距离x距离为2的所有顶点的集合。在本文中，我们证明T包含至少两个顶点x，使得| N〜（++）（x）| ≥| N〜（+）（x）|除非T在双打锦标赛的特殊类别？_（1）中;否则证明T至少包含一个顶点x，使得| N〜（++）（x）| ≥| N〜（？）（x）|并描述两分锦标赛的类？_（2），其中恰好存在一个具有该属性的顶点x;并证明X | = | Y |或| X | ≥4 | Y |，则二分锦标赛T包含一个顶点x，使得| N〜（++）（x）| + | N〜（+）（x）| ≥2 | N〜（？）（x）|。
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