Number of Subgraphs and Their Converses in Tournaments
科研大讨论系列报告
报告题目(Title)： Number of Subgraphs and Their Converses in Tournaments
报告人(Speaker)：雷辉（南开大学）
地点(Place)：腾讯会议 ID： 187 835 488
时间(Time)：2024 年 11 月 1 日（周五） 14:30--15:30
邀请人(Inviter)：徐敏
报告摘要
An oriented graph D is converse invariant if, for any tournament T, the number of copies of D in T is equal to that of its converse −D. El Sahili and Ghazo Hanna [J. Graph Theory 102 (2023), 684-701] showed that any oriented graph D with maximum degree at most 2 is converse invariant. They proposed a question: Can we characterize all converse invariant oriented graphs? In this talk, we introduce a digraph polynomial and employ it to give a necessary condition for an oriented graph to be converse invariant. We characterize all orientations of trees with diameter at most 3 that are converse invariant. In addition, in contrast to the findings of El Sahili and Ghazo Hanna, we prove that every connected graph G with maximum degree at least 3, admits an orientation D of G such that D is not converse invariant. This is joint work with Jiangdong Ai, Gregory Gutin, Anders Yeo, Yacong Zhou.
主讲人简介
雷辉，2019年博士毕业于南开大学，现为南开大学统计与数据科学学院副教授、博士生导师。2022年入选第八届中国科协“青年人才托举工程”项目。主持国家自然科学基金面上、青年各一项、天津市青年基金一项。现担任中国工业与应用数学学会信息和通讯技术领域的数学专委会委员，中国运筹学会宣传工作委员会副秘书长等。
