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 ∈ H. In this article, we give a complete solution to the existence problem of uniform H-factorizations of Kn − I (the graph obtained by removing a 1-factor from the complete graph Kn) for H = {Ch , S(Ch )}, where Ch is a cycle of length an even integer h ≥ 4 and S(Ch ) is the graph consisting of the cycle Ch with a pendant edge attached to each vertex.