On a generalization of the Oberwolfach problem

Let e(1),e(2),... e(n) be a sequence of nonnegative integers Such that the first non-zero term is not one. Let Sigma(i=1)(n) e(i) = (q - 1)/2, where q = p(n) and p is an odd prime. We prove that the complete graph on q vertices can be decomposed into e(1) C-pn-factors, e(2) C-pn (1)-factors,..., and e(n) C-p-factors. (C) 2004 Elsevier Inc. All rights reserved.