Regular factors of simple regular graphs and factor-spectra Original Research Article

Given integers n, r and λ, we determine all values of k for which every simple r-regular graph of order n and with edge-connectivity λ has a k-factor. Using this result we find for k ⩾ 2 the k-spectra Spk(n) = {m: there exists a maximal set of m edge-disjoint k-factors of Kn} which were introduced by Hoffman et al. (1993).