The GENERIC-MST algorithm and the greedy-grow lemma give some guidance for how to find MSTs simply, but they don't immediately suggest efficient algorithms. How do we quickly find cuts and the smallest edges they have?
There are two classic approaches:
Pick a point and grow MST from it. Cut is T vs. V-E.
Sort the edges. Continually add the smallest edge that doesn't create a cycle. Cut is defined implicitly by the smallest edge and the disconnected pieces of T.
