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  "body": "\n## Summary\n\n**Capacitated minimum spanning tree** is a minimal cost spanning tree of a [[graph|00C0BR7D7H]] that has a designated root node $r$ and satisfies the capacity constraint $c$. The capacity constraint ensures that all subtrees (maximal subgraphs connected to the root by a single edge) incident on the root node $r$ have no more than $c$ nodes. If the tree nodes have weights, then the capacity constraint may be interpreted as follows: the sum of weights in any subtree should be no greater than $c$. The edges connecting the subgraphs to the root node are called *gates*. Finding the optimal solution is NP-hard.\n",
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