Cyclic near-Hamiltonian cycle decomposition of 2-fold complete graph

Abstract

In this paper, we formulate the existence of cyclic near-Hamiltonian cycle decomposition of 2Kv, for each odd v > 3. Moreover, a graphical representation for constructing a base cycle for such cyclic near-Hamiltonian cycle decomposition is presented. Then, some examples of this construction for the cases v = 9 and v = 15 are discussed in detail.