Consider a graph graph G with |V| vertices and more than |V|-1 edges, is it possible for an edge to be the 'heaviest' and also be unique, but still be part of the graph's MST? If so, in which cases is it applicable?
From what I've been thinking so far, if the maximum edge is the only part that connects some vertex with the rest of the tree, it has to be part of the MST regardless, but that is regardless of the constraint of having more than |V| - 1 edges.
So am I correct to assume that, having more than |V| - 1 edges you can have the heaviest edge as part of the MST? Also, why is the constraint of edges being more than |V| - 1 applied here, what purpose does it serve?