报告题目：On the sizes of vertex (edge)-k-maximal r-uniform hypergraphs

报告人：田应智教授，新疆大学

报告地点：教室5101

报告时间：10月12日 上午10：50-11：30

摘要：

Let $H=(V,E)$ be a hypergraph, where $V$ is a set of vertices and $E$ is a set of non-empty subsets of $V$ called edges. If all edges of $H$ have the same cardinality $r$, then $H$ is an $r$-uniform hypergraph; if $E$ consists of all $r$-subsets of $V$, then $H$ is a complete $r$-uniform hypergraph, denoted by $K_n^r$, where $n=|V|$. A hypergraph $H'=(V',E')$ is called a subhypergraph of $H=(V,E)$ if $V'\subseteq V$ and $E'\subseteq E$. An $r$-uniform hypergraph $H=(V,E)$ is vetex-$k$-maximal if every subhypergraph of $H$ has vertex-connectivity at most $k$, but for any edge $e\in E(K_n^r)\setminus E(H)$, $H+e$ contains at least one subhypergraph with vertex-connectivity at least $k+1$. Edge-$k$-maximal $r$-uniform hypergraph can be defined similarly. In this talk, we will give some bounds on the sizes of vertex (edge)-$k$-maximal hypergraphs.