Given a directed graph G,a cycle cover is a set of node-disjoint cycles so that each node of G belongs to a cycle. The Cycle Cover Problem asks whether a given directed graph has a cycle cover.
(a) Show that the Cycle Cover Problem can be solved in polynomial time. (Hint: Use Bipartite Matching.)
(b) Suppose we require each cycle to have at most three edges. Show that determining whether a graph G has such a cycle cover is NP-complete.
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