A partial 2k-cycle system of order n can be embedded in a 2k-cycle system of order kn+c(k),k⩾3, where c(k) is a quadratic function of k Original Research Article

The bound for embedding a partial 2k-cycle system of order n, k⩾3, is dramatically improved from kn+d(k)n, where d(k) is a function of k, to kn+c(k), where c(k) is a quadratic function of k. The best known bound for 4-cycles remains 2n+10n.