A disjoint vertex cycle cover of G can be found by a perfect matching on the bipartite graph, H, constructed from the original graph, G, by forming two parts G (L) and its copy G(R) with original graph edges replaced by corresponding L-> R edges.
Is it possible to find a Hamiltonian cycle in G (assuming it exists) as one realization of the vertex-disjoint cycle cover from the bipartite graph, H, using a matching algorithm?