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If the weight of an edge e of cycle C in a graph is larger than the individual weights of all other edges of C, then that edge ________

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If the weight of an edge e of cycle C in a graph is larger than the individual weights of all other edges of C, then that edge ________

(a) belongs to an minimum spanning tree

(b) cannot belong to an minimum spanning tree

(c) belongs to all MSTs of the graph

(d) can not belong to the graph

I had been asked this question in an international level competition.

Query is from Spanning Trees in chapter Trees of Discrete Mathematics

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Correct choice is (b) cannot belong to an minimum spanning tree

For explanation I would say: For any cycle C in the graph, if the weight of an edge e of C is larger than the individual weights of all other edges of C, then this edge cannot belong to an MST.

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