报告题目：On the size-Ramsey number of tight paths

报告人： 陆临渊教授 美国南卡罗兰大学

报告时间：7月11日  上午10:30-11:30

地点：五教5107

摘要：

For any $r\geq 2$ and $k\geq 3$, the $r$-color size-Ramsey number $\hat R(\mathcal{G},r)$ of a $k$-uniform hypergraph $\mathcal{G}$ is the smallest integer $m$ such that there exists a $k$-uniform hypergraph $\mathcal{H}$ on $m$ edges such that any coloring of the edges of $\mathcal{H}$ with $r$ colors yields a monochromatic copy of $\mathcal{G}$. Let $\mathcal{P}_{n,k-1}^{(k)}$ denote the $k$-uniform tight path on $n$ vertices. Dudek, Fleur, Mubayi and R\H{o}dl showed that the size-Ramsey number of tight paths $\hat R(\mathcal{P}_{n,k-1}^{(k)}, 2) = O(n^{k-1-\alpha} (\log n)^{1+\alpha})$ where $\alpha = \frac{k-2}{\binom{k-1}{2}+1}$. In this talk, we improve their bound by showing that $\hat R(\mathcal{P}_{n,k-1}^{(k)}, r) = O(r^k (n\log n)^{k/2})$ for all $k\geq 3$ and $r\geq 2$. (Joint work with Zhiyu Wang)