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数学院:On minimum degree thresholds for fractional perfect matchings

报告题目:On minimum degree thresholds for fractional perfect matchings

报告人:鲁红亮教授,西安交通大学

时间:2018年12月15日 10:00-11:00am 

地点:数学院院楼425

报告摘要:Rodl, Rucinski and Szemeredi determined the minimum $(k-1)$-degree threshold for fractional perfect matchings in $k$-uniform hypergrahs.

For $k-1>d\ge k/2$,  Kuhn, Osthus, and Townsend gave an asymptotic  minimum $d$-degree threshold for fractional perfect matchings in $k$-uniform

hypergraphs. We give the exact $d$-degree threshold when $d\ge k/2$ by proving the following result: Let $n$, $k$, and $d$ be positive integers such that $d\geq k/2$, and let $H$ be a $k$-unifrom hypergraph with order $n$. If $\delta_d(H)>{n-d\choose k-d} -{n-d-(\lceil n/k\rceil-1)\choose k-d}$, then $H$ contains a fractional perfect  matching. Moreover, I will introduce how to obatin a large matching from fractional perfect matching.

学术地点 数学院院楼425 主讲人 鲁红亮教授,西安交通大学
讲座时间 2018年12月15日 10:00-11:00am
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