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An algorithm to enumerate all the elementary circuits of a directed graph is presented. The algorithm is based on a backtracking procedure of Tiernan, but uses a lookahead and labeling technique to avoid unnecessary work. It has a time bound of O ( (V E) (C + 1) ) when applied to a graph with V vertices, E edges, and C elementary circuits.
Robert E. Tarjan (Sat,) studied this question.
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