报 告 人：吴雨泽 博士

报告题目：Structured Codes of Graphs

报告时间：2025年1月9日（周四）下午2:00

报告地点：腾讯会议：394-660-265

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：

       吴雨泽，中国科学技术大学在读博士研究生，师从马杰教授，主要研究方向为图论。

报告摘要：

       We consider the symmetric difference of two graphs on the same vertex set $[n]$, which is the graph on $[n]$ whose edge set consists of all edges that belong to exactly one of the two graphs. Let $\mathcal{F}$ be a class of graphs, and let $M_{\mathcal{F}}(n)$ denote the maximum possible cardinality of a family $\mathcal{G}$ of graphs on $[n]$ such that the symmetric difference of any two members in $\mathcal{G}$ belongs to $\mathcal{F}$. These concepts are recently investigated by Alon, Gujgiczer, K\{o}rner, Milojevi\'{c}, and Simonyi, with the aim of providing a new graphic approach to coding theory. In particular, $M_{\mathcal{F}}(n)$ denotes the maximum possible size of this code.

       In this talk, we will discuss several problems related to $M_{\mathcal{F}}(n)$ in general settings and the relationship between them and other Combinatorial problems.