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Here s a proposal for how to find the length of the shortest cycle in an undirected graph with unit edge lengths. When a back
Heres a proposal for how to find the length of the shortest cycle in an undirected graph with unit
edge lengths.
When a back edge, say v w is encountered during a depthfirst search, it forms a
cycle with the tree edges from w to v The length of the cycle is levelv levelw
where the level of a vertex is its distance in the DFS tree from the root vertex. This
suggests the following algorithm:
Do a depthfirst search, keeping track of the level of each vertex.
Each time a back edge is encountered, 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 counterexample as well as a brief
one or two sentence explanation
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