Cyclic Hamiltonian cycle systems of the lambda-fold complete and cocktail party graphs

摘要

We establish the necessary and sufficient conditions for the existence of a cyclic Hamiltonian cycle system of lambda K(v) and of lambda(K(2v) - I). We also consider the existence problem for cyclic Hamiltonian cycle systems of lambda K(v) that are simple, i.e., without repeated cycles, solving it in the case that v is a prime. (C) 2010 Elsevier Ltd. All rights reserved.