导　　师： 吴康

学科专业： D0102

授予学位： 硕士

作　　者： ;

机构地区： 华南师范大学

摘　　要： ramsey问题是组合数学、离散数学、图论、算法研究领域的著名难题和热门课题.ramsey理论在上述各数学分支上所处的地位举足轻重.该文度图对ramsey型问题进行综合处理、分类讨论,初步探讨其在竞赛数学中的应用.首先,在介绍ramsey理论研究背景的基础上,探讨了ramsey型问题的构成,并论述了在竞赛数学中研究ramsey型问题的必要性.然后,对在数学竞赛中所遇到的有关ramsey型问题的基本理论以及处理这类图的染色问题的一些基本技巧,从10个方面进行了综合处理和分类讨论.最后,作者针对将ramsey理论的前沿结果转化为ramsey型问题以及其在竞赛数学中的应用,提出了一些个人见解. Ramsey problems are not onCy famous but aCso hot anddifficult problems among Combinatorics, /(Discrete Mathematics, Graph Theory and Computational Method. The /(Ramsey theory plays an important role in above each branch of mathematics, This thesis intends to study the /(Ramsey-type problems by classifying and discussing for their preliminary application in the Competition Mathematics. Firstly, on the Basis of introducing the background knowledge of the Ramsey theory, it explored the composing of /(Ramsey-type problems, and discussed the necessity of studying /(Ramsey-type problems in the Competition Mathematics. Secondly, it analysedandinvestigatedthe basic theory and some skiffs of /(Ramsey-type problems met in the Competition Mathematics in 10 aspects. Finally, aiming at the applications of the advanced results of /(Ramsey problems in the Competition Mathematics, the researcher suggested some personal opinions.

关 键 词： 数 型问题 竞赛数学 染色问题

分 类 号： [G424.28]

领　　域： [文化科学] [文化科学] [文化科学]