# Tagged Questions

Hypergraphs are generalizations of graphs, where edges can be made of more than two vertices.

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### Hypergraph clustering conductance Formula

Consider the Hypergraph $H=(V,E)$, with $V$ being the vertices and $E$ being the hyperedges. What is the formula of conductance $\Phi(S)$ for hypergraphs, with $S$ being a set of vertices (cluster ...
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### Tree decompositions in linear hypergraphs

A linear hypergraph is a pair $\pi=(X, L)$ where $X\neq \emptyset$ is a finite set and $L\subseteq {\cal P}(X)$ has the following properties: for $e\in L$ we have $|e|\geq 2$; if $e_1\neq e_2 \in L$ ...
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### Minimality condition in a certain class of hypergraphs

A hypergraph is a pair $H=(V,E)$ such that $V$ is a (possibly infinite) set and $E\subseteq \mathcal{P}(V)$. $C\subseteq E$ is said to be a cover if $\bigcup C = V$ and $C$is minimal if $C'\subseteq C$...
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### Strongly minimal covers

Let $H=(V,E)$ be a hypergraph, that is $V$ is a set and $E\subseteq \mathcal{P}(V)$. We say that $C\subseteq E$ is a cover of $H$ if $\bigcup C = V$. A cover $M\subseteq E$ is said to be strongly ...
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### Optimal tiling for a collection of partitions

I'm interested in a possible generalization of Tiling relation on the set of partitions (the question has only been partially answered). Let $x$ be an infinite set and let $\text{Part}(x)$ be the ...
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### The category of hypergraphs as a topos

It seems known that the category of hypergraphs is a topos. I am looking for any reference here, or just a statement of this in the literature, but can't find anything. There is one paper A ...
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### Maximum number of hyperedges in a directed hypergraph

I need a formula for maximum number of hyperedges that a directed hypergraph with n vertices can have. Following point is an unresolved issues for me and it keeps coming back to my mind: There are ...