Study On Vertex-disjoint Cycles Containing Independent Edges In Bipartite Graphs

A set of cycles in G is said to be disjoint,if and only if there is no common vertex between any two of them.The existence of disjoint cycles is a vital area of graph.This paper mainly studies the existence of disjoint 6-cycles and 8-cycles containing specified edges in bipartite graphs.This paper consists of three chapters.In chapter 1,we introduced the notations and termi-nologies are involved in this paper,then we summarized the background of the problems stud-ied in this paper.In chapter 2,we studied the existence of disjoint 6-cycles containing specified edges in a bipartite graph.Our result is as follows:let G=(V1,V2;E)be a bipartite graph with|V1|=|V2|=n=3k,where k is a positive integer,we verified that if ?(G)?3k/2+k,then for any k independent edges e1,e2,…,ek in G,G contains k disjoint 6-cycles C1,C2,…,Ck,such that e1 ?(Ci),1?i?k.In chapter 3,we proved that if G(V1,V2;E)is a bipartite graph with|V1|=|V2|=4k,and 5(G)>3k,then for any k independent edges e1,e2,…,ek in G,G contains k disjoint cycles of order 8 that admit e1,e2,…,ek.Finally,we proposed further problems that can be discussed.