报 告 人：胡平 副教授
报告题目：On short directed cycles in triangle-free digraphs
报告时间：2025年5月7日（周四）下午2：00
报告地点：腾讯会议：505-447-503
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
胡平，本科毕业于北京大学数学系，2014年8月在美国伊利诺伊大学香槟分校获得数学博士学位，2014年10月至2017年8月在英国华威大学任研究员，2017年入职中山大学任副教授。研究领域包括Ramsey理论和Turán理论等。在JCTB, RSA, CPC, JGT, EJC等期刊杂志发表论文多篇。主持国家自然科学基金青年、面上项目各一项。
报告摘要：
Seymour and Spirkl considered a bipartite version of the Caccetta-Häggkvist Conjecture. They conjectured that if G is a bipartite digraph with n vertices in each part, and every vertex has out-degree more than n/(k+1), then G has a directed cycle of length at most 2k. And they proved this for k=1,2,3,4,6 and k at least 224539. Since bipartite is without all odd cycles, we consider a strengthening of this conjecture by changing bipartite to triangle-free. We show that for k at most 5, if G is a n-vertex digraph without transitive triangle, and every vertex has out-degree more than n/(k+1), then G has a directed cycle of length at most k.