Uniform (C_k, P_k+1)-Factorizations of Kn − I When k Is Even

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 for uniform (C_k, P_k+1 )-factorizations of K_n − I in the case when k is even.