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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 (Ck,Pk+1)-factorizations of Kn−I in the case when k is even.

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