Speaker：Yandong Bai (Northwestern Polytechnical University)

Time：2024-1-9, 16:30

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

An oriented graph is a digraph without 2-cycles. Seymour’s Second Neighborhood Conjecture (SSNC) states that every oriented graph has a vertex satisfying that the cardinality of its second out-neighborhood is not less than that of its first out-neighborhood. A digraph is k-anti-transitive if, for every two vertices u and v, the existence of a directed (u,v)-path of length k implies that u does not dominate v. If SSNC were ture for k-anti-transitive oriented graphs for an arbitrary k, then it would hold for general finite oriented graphs, as every finite oriented graph is k-anti-transitive for k greater than the length of its longest path. So far, SSNC has been verified for k-anti-transitive oriented graphs with k⩽6. We show that SSNC holds for 7-anti-transitive oriented graphs.