关于二部有向图哈密顿性的Meyniel条件
On the Meyniel condition for hamiltonicity in bipartite digraphs
摘要：
本文证明了平衡二部有向图的Hamilton性的一个Meyniel型判别准则：对于k大于或等于2，色类为k的二部有向图D是Hamilton的，如果对每一对顶点u，v，使得D不含弧uv和vu，则顶点u和v的度之和至少为3 k +1.由此，我们得到了关于最小度的哈密尔顿性的一个尖锐的充分条件：2k个顶点的平衡二部有向图D是哈密尔顿的，如果它的最小度至少是（3 k + 1）/2.
英文摘要：
We prove a sharp Meyniel-type criterion for hamiltonicity of a balanced bipartite digraph: For k greater than or equal to 2, a bipartite digraph D with colour classes of cardinalities k is hamiltonian if the sum of degrees of vertices u and v is at least 3k+1 for every pair of vertices u, v such that D does not contain the arc uv nor vu. As a consequence, we obtain a sharp sufficient condition for hamiltonicity in terms of the minimal degree: a balanced bipartite digraph D on 2k vertices is hamiltonian if its minimal degree is at least (3k + 1)/2.
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