Generalized Spanning Trees

A spanning tree of an undirected, connected graph (V,E) with vertex set V and edge set E is a subset of edges F such that the graph (V,F) is connected and has no cycles. After a few moments thought, one realizes that an equivalent way to say this is to say: - 1) |F| = |V| - 1 - 2) For any non-empty subset of nodes S, the number of edges with both endpoints in S is does not exceed |S|-1. There