报告题目：On vertex-disjoint cycles in digraphs

报告人：Yandong Bai

Department of Applied Mathematics, Northwestern Polytechnical University

报告时间：4：10-5：10

报告地点：1418

摘要：

Bermond and Thomassen conjectured in [J. Graph Theory 5 (1) (1981) 1-43] that every digraph with minimum outdegree at least 2k−1 contains k vertex-disjoint cycles. This is one of the 100 famous conjectures selected by Bondy and Murty in their well-known book “Graph Theory (3rd Edition)”. Lichiardopol conjectured in [SIAM J.

Discrete Math. 28 (3) (2014) 1618-1627] that there exists an integer g(k) such that every digraph with minimum outdegree at least g(k) contains k vertex-disjoint cycles of distinct lengths. This talk will focus on the above two conjectures and consider the existence of vertex-disjoint cycles with and without length constraints in digraphs.

Some important known results for general digraphs and our recent work on bipartite tournaments and multipartite tournaments will be given.