报告题目:Improved  Bound on Vertex Degree Version of Erd\H{o}s Matching Conjecture

报告人：鲁红亮 （西安交通大学 教授）

报告时间：4月15号下午 4:00--4:45 

地点：管理楼1418

报告摘要：For a $k$-uniform hypergraph $H$, let $\delta_1(H)$ denote the minimum vertex degree of $H$, and $\nu(H)$ denote the size of a maximum  matching in $H$. In this paper, we   show that for sufficiently large integer $n$ and integers  $k\geq 3$ and $m\ge 1$, if $H$ is a $k$-graph with $|V(H)|=n\geq 2mk$ and $\delta_1(H)>{{n-1}\choose {k-1}}-{{n-m}\choose {k-1}},$ then   $\nu(H)\geq m$. This improves upon an earlier result of Bollob\'{a}s, Daykin  and Erd\H{o}s (1976) for the range $n> 2k^3(m+1)$.