In the evening of July 14 2021. Professor Dong Ye from Middle Tennessee State University gave an online report entitled “Perfect Theorem and Applications”. Xingqin Qi hosted this report, teachers and graduate students of our school attended this report online.

The well-known Menger Theorem says a graph G is k-connected if and only if for any two vertices x and y, there are k internally disjoint (x, y) paths in G. Perfect Theorem strengthens Menger theorem in a such way that, for a vertex x and a set S of vertices with at least k vertices, if G has an k-(x, S)-fan, then any (k-1)-(x, S)-fan can be extended to a k-(x, S)-fan such that the end vertices of the (k-1)-(x S)-fan are reserved as end vertices in the k-(x, S)-fan, In this talk, Dr. Ye focued on Perfect Theorem and it’s generalizations and some applications on cycalibility and linkage problems. From this talk teachers and students all obtained better understandings of Perfect Theorem, and benefit a lot.

The successful holding of this report has strengthened atmosphere in researching probability theory in our school. and deepened the friendship and cooperation between the two sides.