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)
