On the cyclic decomposition of complete multigraph into near Hamiltonian cycles

摘要

Let v and λ be positive integer, λK_v denote a complete multigraph. A decomposition of a graph G is a set of subgraphs of G whose edge sets partition the edge set of G. In this article, difference set method is used to introduce a new design that is decomposed a complete multigraph into near Hamiltonian cycles. In course of developing this design, a combination between near-4-factor and a cyclic (v - 1)-cycle system of 4K_v, when v = 4n + 2, n > 2, will be constructed.