A minimum bottleneck spanning tree is not always a minimum spanning tree, but a minimum spanning tree is always a minimum bottleneck spanning tree. Correct For the positive statement, recall the following (from correctness of Prim’s algorithm): for every edge e of the MST, there is a cut (A,B) for which e is the cheapest one crossing it.

1 Minimum Directed Spanning Trees. Let G = (V, E, w) be a weighted directed graph, where w : E → R Instead of wanting a minimum spanning tree, we can also ask for a maximum spanning tree. For example, if in the example of Figure 6 we would like to nd the MDST rooted at δ, undoing all...

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