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A brief description and comparison of all known algorithms for enumerating all circuits of a graph is provided, and upper bounds on computation time of many algorithms are derived. The vector space method of circuit enumeration is discussed. It is proved that K₃ ,K₄ ,K₄ - x and K3,3 are the only undirected and reduced graphs which do not have any edge-disjoint unions of circuits.
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Mateti et al. (1976) studied this question.
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