On a generalization of the Oberwolfach problem

Let e1,e2,…,en be a sequence of nonnegative integers such that the first non-zero term is not one. Let ∑i=1n ei=(q−1)/2, where q=pn and p is an odd prime. We prove that the complete graph on q vertices can be decomposed into e1 Cpn-factors, e2 Cpn−1-factors, …, and en Cp-factors.