# Can the heaviest edge ever be in an MST?

Is it true that the heaviest edge in a directed graph can not be in the MST of that graph?

I don't think it is true because we might end up with a heaviest edge that is not part of a cycle.

Can anyone confirm?

• Let $G$ be a graph with a bridge. – Pål GD May 9 '13 at 15:24

No, it is not true. Consider a graph with 2 vertices and an edge between them. This is the heaviest edge, and it will be in the minimum spanning tree of $G$.