Assume we have non-distinct edge weights and multiple Minimum Spanning Trees may exist.
If we are given an edge, from A-B, how can we check (in linear time) if this edge is part of some MST?
Right now, I am considering a solution based on the cycle property. We look at all the edges with a weight less than our edge under consideration. If we can build a path utilizing the smaller edges via Depth First Search, we can say that our edge is not part of any MST.
Is my method correct?
If not, should I be looking at something else?