I don't know if that's the most accurate title.
I'm trying to prove that one property of trees implies another without using any of the other properties.
This is for homework. But I'm really just curious if the proof was this easy or if someone more clever can find glaring holes. I will cite any help I receive. I'm a CS guy that doesn't have much experience writing proofs.
The graph G is connected, but removing any edge disconnects the graph implies that any two vertices in G are connected by a unique simple path.
My proof is this:
Suppose that the G is not connected by a unique simple path. Then there must exist some edge that could be removed without resulting in a disconnected graph.
Does this work?