Heres a proposal for how to find length of shortest cycle in an undirected graph with unit edge lengths. When a back edge, say(v,w) is encountered during a depth first search, it forms a cycle with the tree edges from w to v. The length of cycle is level[v] - level[w] + 1, where the level of vertex is its distance in DFS tree from root vertex. This suggests the following algorithm: (a) Do a depth-first search, keeping track of level of each vertex. (b) Each time a back edge is countered, compute the cycle length and save it if it is smaller than the shortest one previously seen.

Show that this strategy does not always work by providing a counter example as well as explanation.