Let G be a graph with n vertices each of which has degree at

Let G be a graph with n vertices, each of which has degree at least 3. Assuming that there are no cycles of length less than m, show that for each v belongs to G that there are at least 2^m paths of length m starting at v.

Solution

We have seen the Erdos-Stone theorem which says that given a forbidden subgraph H, the extremal number of edges is ex(n, H) = 1 2 (11/((H)1)+o(1))n 2 . Here, o(1) means a term tending to zero as n . This basically resol