| An m-cycle system of the graph G is a partition of E(G) such that each clement of the partition is a m-cyclc of G. Cycle systems of graph is a hot topic in graph and has received a lot of attention in recent years. This paper generalized the result that Schgal and Rodger made about the4-cyclc system of Kn-F, where F is a2-rcgular lcave. This paper give the necessary and sufficient conditions for the existence of a6-cycle system of a complete graph on n vertices with a nearly2-rcgular leave.This paper consist of the following three parts:In the first chapter, some basic notations and current home and abroad research of6-cycle systems are introduced, and also some symbols and the main result are given.In the second chapter, we construct a lot of small order of cycles and some special cases of6-cycle system.In the third chapter, we prove the6-cycle system of a complete graph on n vertices with a nearly2-rcgular leave. The construction that are given in the chapter2is used in this chapter, then the main result by induction is obtained. |
