On m-cycle holey systems

摘要

Let G_u~v denote the graph K_vK_u if both u and v are odd, and (K_v - F_1)(K_u - F_2) if both u and v are even, where F_1 is a 1-factor of K_v and F_2 is a 1-factor of K_u with F_2 ? F_1. In this paper, we study the existence problem of m-cycle design of G_u~v. By using direct and recurssive constructions, we obtain several new m-cycle design of G_u~v.