Study of Ramsey-type decomposition problems

点击翻译按钮获取中文摘要

Ramsey-type problems in discrete mathematics and combinatorics are to determine whether the following claims hold or not in various situations; any sufficiently large structure, however it is in disorder, has a local structure that is in order.In this study, Ramsey-type partition problems are introduced. They are deeply connected with Ramsey-type problems, and our aim is to investigate the following claim; any sufficiently large structure, however it is in disorder, admits a partition that is in order. We have shown some theorems for the Ramsey-type partition problems of some discrete structures, such as graphs.