The Two Circle In The Tournament

Graph theory is a component of mathematics, which is mainly about the study of graph. The graph in graph theory consists of a set of points together with lines joining certain pairs of these points. This kind of graph is usually used to describe certain relations of some things, in which points stand for things and lines stand for the relations between the things.Research on graph theory of modern mainstream direction is directed graph. In the area of directed graph research, the nature of the plan Hamilton is a study to map the core content. Directed Graph Hamilton Circle can be seen as a continuation of the Euler tour, but so far the plan nontrivial Hamilton necessary and sufficient conditions are not found in graph theory, it is not yet one of the main issues to resolve. For more than a century, there has been different from the perspective of research on that question by a lot of the full judgement Hamilton graph conditions, such as Ore famous theorem, Fan-type conditions, as well as Chvatal in 1972 with the plan of the sequence diagram judgement Hamilton a sufficient condition (and is a class of great Hamilton). Tournament is a very useful to have plans for the Study of Hamilton has a very important significance. Bipartite tournament is a typical and special category in tournaments, its nature Hamilton also has an important role.In this paper, the Hamiltonian qualities in Bipartite tournament are studied. On the basis of two new sufficient conditions brought up by Wang Jian-zhong that Bipartite tournament would be directed Hamiltonian graph and a sufficient and essential condition brought up by an associate professor Li Gui-rongXu that Bipartite tournament would be directed Hamiltonian graph and results of other forfathers, the sufficient conditions about Bipartite tournament with directed Hamiltonian graph are shown. In addition, we try to find and prove some characters on the cycles in some special bipartite tournament, some satisfied results are gained.This thesis consists of 4 chapters. In the first chapter, we will introduce the background as the basic concepts, and main results obtained in this thesis is liven.In the second chapter, the terminology and notations on graph theory are introduced.In the third chapter, We prove a new sufficient condition for Hamiltonian cycles in Bipartite tournaments, which are listed as follows: if an n x n bipartite tournament T satisfies the conditions W(n—3), then T is Hamiltonian, except for four exceptional graphs. In the last chapter, we find and prove some characters on the cycles in a special kind of bipartite tournament.