极大局部边连通和超级局部边连通二部有向图的邻域条件

本文主要证明了对于n阶二部有向图D，当最小度δ≥3,对任意同部顶点x，y,有min{|N⁺(x)∪N⁺(y)|，|N^-(x)∪N^-(y)|}≥(n+3)/4]时,D为极大局部边连通的；当最小度δ≥4,对任意同部顶点x，y,有min{|N⁺(x)∪N⁺(y)|,|N^-(x)∪N^-(y)|}>(n/4)+1时,D为超级局部边连通的。我们证明了条件的最好可能性及结果与原有结果的独立性。

Neighborhood conditions of maximally local-edge-connected and super-local-edge-connected bipartite digraphs

We prove that an-order bipartite digraph D is maximally local-edge-connected if the minimum degree δ≥3 and min{|N+(x)∪N+(y)|,|N-(x)∪N-(y)|}≥n+3/4 for each pair of verticesx andy in the same part,and is super-edge-connected if δ≥4 and min{|N+(x)∪N+(y)|,|N-(x)∪N-(y)|}>n/4+1 for each pair of verticesx andy in the same part.We also prove that the best possibility of the conditions and the independence of the results from the primitive ones.