Small embeddings for partial cycle systems of odd length

AbstractWe prove that if m is odd then a partial m-cycle system on n vertices can be embedded in an m-cycle system on at most m((m − 2)n(n − 1) + 2n + 1) vertices and that a partial weak Steiner m-cycle system on n vertices can be embedded in an m-cycle system on m(2n + 1) vertices