Uniform {Ch,S(Ch)}-Factorizations of Kn-I for Even h

Let H be a connected subgraph of a graph G. An H-factor of G is a spanning subgraph of G whose components are isomorphic to H. Given a set H of mutually non-isomorphic graphs, a uniform H -factorization of G is a partition of the edges of G into H-factors for some H is an element of H. In this article, we give a complete solution to the existence problem of uniform H -factorizations of K-n - I (the graph obtained by removing a 1-factor from the complete graph K-n) for H = {C-h, S(C-h)}, where C-h is a cycle of length an even integer h >= 4 and S (C-h) is the graph consisting of the cycle C-h with a pendant edge attached to each vertex.