| The graph theory is progressing rapidly. One striking feature is the inventionof modern methods. More and more methods from algebra, geometry, probability,and analysis are employed. As an important area of graph theory, graph Ramseytheory also has been developed greatly following the appearance of these methods.Ramsey Theory refers to the study of partitions of large structures. Typical resultsstate that a certain substructure must occur in some classes of the partition. Thatis to say, complete disorder is impossible. The smallest size of the large structureis called Ramsey number.In order to understand graph theory deeply, researchers introduced manyscales, such as Ramsey number, bipartite Ramsey number, size Bipartite Ramseynumber and so on.This dissertation is devoted to bound the Bipartite Ramsey numbers of someeven cycles vs. stars, which is divided into two parts. Chapter one is an intro-duction, in which basic definitions and related concepts are given. In Chaptertwo, first, the bounds of br({C4, C6}, K1,n) are obtained, and the exact value ofbr({C4, C6}, K1,n) for infinitely many n are determined. Secondly, we give the up-per bound of br(C4, K1l,n), and prove that the exact value of br(C4, K1,n) is q2-1or q2 for n=q2-q, where q is a prime power. |
