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Hypergraphs are like simple graphs, except that instead of having edges that only connect 2 vertices, their edges are sets of any number of vertices. This happens to mean that all graphs are just a ...

A hypergraph is a pair $H=(V,E)$ where $V\neq \emptyset$ is a set and $E\subseteq{\cal P}(V)$ is a collection of subsets of $V$. We say two hypergraphs $H_i=(V_i, E_i)$ for $i=1,2$ are isomorphic if ...

The following theorem is a classical result (see [Alon and Spencer, The probabilistic method, 2nd ed., Theorem 1.2.2]): Theorem: Let $G$ be a graph on $n$ vertices with minimum degree $d$. Then $G$ ...

I guess a discrete-mathematics-related question is still welcome in MO since I was new to the community and learned from this amazing past post. The following claim is a simplified and abstract form ...

A complete linear hypergraph is a hypergraph $H=(V,E)$ such that $|e|\geq 2$ for all $e\in E$, $|e_1\cap e_2|=1$ for all $e_1, e_2\in E$ with $e_1\neq e_2$, and for all $v\in V$ we have $|\{e\in E:v\...