港澳六宝大全

讲座名称：The emergence of a giant rainbow component in random coloured graphs

讲座人：Do Tuan Anh

讲座时间：4月28日10:00-11:00

讲座地点：长安校区网安大楼A-1236

讲座人介绍：

Dr. Do Tuan Anh graduated with a PhD from Graz University of Technology in 2023. Since 2024, he has been at Beijing Institute of Technology (BIT) as a Postdoc in a combinatorics group led by Prof. Jie Han. His research mainly concerns probabilistic and extremal combinatorics. He has publications in the SIAM Journal on Discrete Mathematics, the European Journal of Combinatorics, the Journal of Graph Theory, and the Electronic Journal of Combinatorics

Do Tuan Anh博士于 2023 年毕业于格拉茨工业大学，获博士学位。2024 年起，他在北京理工大学从事博士后研究，合作导师为韩杰教授，隶属组合数学研究团队。其研究方向主要为概率组合与极值组合理论，研究成果发表于《SIAM 离散数学期刊》《欧洲组合数学期刊》《图论杂志》及《组合数学电子期刊》等期刊。

讲座内容：

The random coloured graph $G_c(n,p)$ is obtained from the Erd\H{o}s-R\'{e}nyi binomial random graph $G(n,p)$ by assigning to each edge a colour from a set of $c$ colours independently and uniformly at random. It is not hard to see that, when $c = \Theta(n)$, the order of the largest rainbow tree in this model undergoes a phase transition at the critical point $p=\frac{1}{n}$. In this talk, we determine the asymptotic order of the largest rainbow tree in the \emph{weakly supercritical regime}, when $p = \frac{1+\eps}{n}$ for some $\eps=\eps(n)>0$ which satisfies $\eps = o(1)$ and $\eps^3 n\to\infty$. We show that with high probability the giant component of $G_c(n,p)$ contains an almost spanning rainbow tree. We also consider the order of the largest rainbow tree in the \emph{sparse regime}, when $p = \frac{d}{n}$ for some constant $d >1$. In particular we show that for any $\delta >0$ there is some $d$ such that if $c\ge n$, with high probability $G_c(n,d/n)$ contains an almost spanning (of length at least $(1-\delta)n$) rainbow cycle. This is a joint work with Cooley, Erde and Missethan.

主办单位：信息交叉学部