On finding hypercycles in chemical reaction networks

Directed hypercycles have recently been used to model chemical reaction networks. We present an NP-completeness proof for the problem of finding a hypercycle in a directed hypergraph. This sheds some light to some open questions posed by Zeigarnik [A.V. Zeigarnik, On hypercycles and hypercircuits in hypergraphs, in: Discrete Mathematical Chemistry, in: DIMACS Series in, Discrete Mathematics and Theoretical Computer Science, vol. 51, AMS, 2000, pp. 377–383] who modelled chemical reactions by directed hypergraphs.