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Starting point. For every simple, undirected graph $G=(V,E)$ there is $E_0\subseteq E$ such that $(V,E_0)$ is minimally connected: the spanning tree. The goal of this question is to find out whether ...

Although every connected graph has a spanning tree, the same is not true for hypergraphs: consider the hypergraph on 4 vertices with all possible edges of size 3. You need to pick at least two edges ...