Minimum spanning tree formulation
The constraint expresses the following fact:


  Let $T$ be a spanning tree, and suppose that we partition the vertex set into $r$ parts. There are exactly $r-1$ edges of $T$ which connect different parts.


For example, if $T$ is a tree and $C,\overline{C}$ is a cut, then exactly one edge of $T$ crosses the cut, that is, connects $C$ and $\overline{C}$.