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A pair $(V,\mathbb{E})$ is said to be finite uniform intersecting hypergraph, where $V$ is a non-empty finite set, $\mathbb{E}\subset\binom{V}{k}$ for some integer $k\geq2$ and for each $B$ and $B'\in\mathbb{E}$, $B\cap B'\neq\emptyset$. Here for each integer $k\geq2$, the set of all subsets of $V$, with size $k$ is denoted as $\binom{V}{k}$. An example of such hypergraph is if we take $V=[2k-1]$ and $\mathbb{E}=\binom{[2k-1]}{k}$, where $[2k-1]=\{1,2,\ldots,2k-1\}$. In a finite hypergraph, $(V,\mathbb{E})$, a \emph{transversal} is a subset $T$ of $V$, which intersects all the members of $\mathbb{E}$ and if $C$ intersects all the members of $\mathbb{E}$, then $|T|\leq|C|$. For example, each
$C\in\binom{[2k-1]}{k}$ is a transversal for the aforementioned example. In this talk, we explain that a transversal is an useful tool to read a maximal uniform intersecting hypergraph. |