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Vertex cycle cover
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Vertex cycle cover : ウィキペディア英語版
Vertex cycle cover
In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph ''G'' is a 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''. A disjoint cycle cover of an undirected graph (if it exists) can be found in polynomial time by transforming the problem into a problem of finding a perfect matching in a larger graph.〔.〕
〔http://www.cs.cmu.edu/~avrim/451f13/recitation/rec1016.txt (problem 1)〕
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.
==Properties and applications==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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