On vertex-primitive s-arc-transitive digraphs
报告题目(Title)：On vertex-primitive s-arc-transitive digraphs
报告人(Speaker)：尹富纲 副教授（北京交通大学）
地点(Place)：后主楼1220
时间(Time)：2026年9月18日（周五）15:30-16:30
邀请人(Inviter)：徐敏
报告摘要
A digraph is a directed graph where each edge has only one direction. An s-arc in a digraph is a sequence of s+1 vertices (v0, v1, …, vs) such that vi → vi+1 for all 0 ≤ i < s (that is, (vi, vi+1) is an arc). For any two s-arcs (v0, v1, …, vs) and (u0, u1, …, us) in a digraph Γ, if there exists an automorphism g of Γ such that vig = ui for all 0 ≤ i ≤ s, then Γ is called an s-arc-transitive digraph. The existence of vertex-primitive 2-arc-transitive digraphs was a long-standing open problem. It remained unresolved until 2017, when Giudici, Li, and Xia discovered an infinite family of such digraphs (JCTB). They raised the question of whether there exists an upper bound on s for vertex-primitive s-arc-transitive digraphs that are not directed cycles. This question has been reduced to the almost simple group cases, and progress has been made for several families of simple groups. In this talk, I will introduce advancements in addressing the upper bound problem for s, and introduce new construction of vertex-primitive 2-arc-transitive digraphs.
主讲人简介
尹富纲，北京交通大学，高聘副教授。主要从事代数图论方面的研究，研究兴趣主要有s-弧传递图和凯莱图。发表论文近30篇，一些成果发表在Trans. Amer. Math. Soc., JCTA/B, J. Algebra, J. Graph Theory等期刊。主持国家自然科学基金青年基金项目和面上项目。
