報(bào) 告 人：吳雨澤 博士

報(bào)告題目：Structured Codes of Graphs

報(bào)告時(shí)間：2025年1月9日（周四）下午2:00

報(bào)告地點(diǎn)：騰訊會(huì)議：394-660-265

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院 

報(bào)告人簡介：

       吳雨澤，中國科學(xué)技術(shù)大學(xué)在讀博士研究生，師從馬杰教授，主要研究方向?yàn)閳D論。

報(bào)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.