Prove that if G is a connected, weighted graph and e is an edge of G that (1) has greater weight than any other edge of G and (2) is in a circuit of G, then there is no minimum spanning tree T for G such that e is in T.
When is a connected weighted graph and is an edge of which is in a circuit of and that has larger weight than any other edge of graph , then there exists no minimum spanning tree for such that the edge e is in .
Distinct minimum spanning trees.
contains a nontrivial circuit.
Suppose that there is a minimal spanning tree such that .
Note that is an edge of and has larger weight than any other edge.
It is in a circuit of .
Let be another tree which has the same edges as in except
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