Decomposition of Km,n(Km,n1) into cycles (circuits) of length 2k

In this paper we give necessary and sufficient conditions in order that K_m,n ($\text{K}{}_{\mathrm{m,n}}{}^1$) admits a decomposition into 2k-cycles (2k-circuits). This answers conjectures of J. C. Bermond (Thesis, Paris XI (Orsay), 1975) and J. C. Bermond and V. Faber (J. Combinatorial Theory Ser. B21 (1976), 146–155).