Hi I have two problems I need help with.

1) Prove that if G is a connected simple graph and e is an edge of a simple circuit in G then the graph G without the edge e is still connected.

So, this is what i thought: Since by definition of a connected graph, a connected graph is connected if there is a path between every pair of vertices of the graph. So by removing the edge e, the remainding graph is still connected.

Can someone help me out on this, I dont think thats a correct proof.

This next question puzzles me and I have even tried drawing it to help my understanding but I stil ldont get it.

2) Let G be a directed graph with n vertices. Assume that for vertices x and y in G there is a path from x to y such that the length of the path is greater than or equal to n.

So the question is why is there infinitely many paths from x to y.

Someone please help me out on this one.

Thanks,

Kurac.