Generating all cycles, chordless cycles, and Hamiltonian cycles with the principle of exclusion

An efficient method to generate all edge sets X⊆EX⊆E of a graph G=(V,E)G=(V,E), which are vertex-disjoint unions of cycles, is presented. It can be tweaked to generate (i) all cycles, (ii) all cycles of cardinality ⩽5, (iii) all chordless cycles, (iv) all Hamiltonian cycles.