Cyclically decomposing the complete graph into cycles

Abstract

Let m(1), m(2),..., m(k) be positive integers not less than 3 and let n = Sigma(i=1)(k) m(i). Then, it is proved that the complete graph of order 2n + 1 can be cyclically decomposed into k(2n + 1) cycles such that, for each i = 1, 2,...,k, the cycle of length mi occurs exactly 2n + 1 times. (C) 2003 Elsevier B.V. All rights reserved.