On Algorithms for Enumerating All Circuits of a Graph
Prabhaker Mateti, Narsingh Deo · SIAM Journal on Computing · 1976
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 $K_3 ,K_4 ,K_4 - x$ and $K_{3,3} $ are the only undirected and reduced graphs which do not have any edge-disjoint unions of circuits.