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A form of Hadwiger's conjecture for hypergraphs

A hypergraph $H=(V,E)$ consists of a set $V$ and $E\subseteq {\mathcal P}(V)$. If $S\subseteq V$, we define $$E|_S = \{e\cap S: (e\in E) \land (e\cap S \neq \emptyset)\}$$ and call $(S, E|_S)$ the ...
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