High Quality Content by WIKIPEDIA articles! In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph is the set of cycles which are subgraphs of G and contain all vertices of G. If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. In this case the set of the cycles constitutes a spanning subgraph of G. If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover. Similar definitions may be introduced for digraphs, in terms of directed cycles. The permanent of a 01-matrix is equal to the number of cycle covers of a directed graph with this adjacency matrix. This fact is used in a simplified proof of the fact that computation of the permanent is #P-complete.

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