Given a connected graph with minimum degree 3 and a set of edges in this graph, I wish to find the number of decompositions of this edge set into cycles of the graph. I use decompositions in the sense that an edge in the set can be part of multiple cycles that the set is decomposed into. I know that this edge set is constructed by taking the union (not disjoint) of cycles of the graph, but I want to know how many other possible sets of cycles I could have taken the union of to get the same edge set. This might not be analytically possible but an algorithm to do this would be awesome.
Unions of edge sets of cycles in a graph
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graph-theory
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0You're after an [edge cycle cover](http://en.wikipedia.org/wiki/Edge_cycle_cover) of your graph (rather than a "decomposition"). – 2012-11-01