1. ## contrapositive proof

prove that for every connected graph G, if G has no cycles then for every pair of vertices a,b in G, there is only one path from a to b in G.

the contrapositive of this would be easier to prove but i'm not exactly sure how to do that..

2. Originally Posted by mathh18
prove that for every connected graph G, if G has no cycles then for every pair of vertices a,b in G, there is only one path from a to b in G.
the contrapositive of this would be easier to prove but i'm not exactly sure how to do that..
Well what is a cycle?
Is every path from a to b also a path from b to a?
What happens if there are two paths from a to b?

3. a cycle is a circuit with the only repeated nodes at the beginning and end.
every path from a to b is also a path from b to a
if there are two paths from a to b, then...there is more than one cycle?

4. Originally Posted by mathh18
if there are two paths from a to b, then...there is more than one cycle?
What? How is that?
How is there at least one cycle?

5. I don't know I'm confused. Does it mean there is one cycle?

6. Originally Posted by mathh18
I don't know I'm confused. Does it mean there is one cycle?
Yes it does. But how?

7. That's what I'm confused on