Ramsey Theory, Hypergraph Coloring, and Structural Problems in Graph Theory

拉姆齐理论、超图着色和图论中的结构问题

• 批准号: 0233777
• 负责人: Dhruv Mubayi
• 金额: $ 0.42万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-01 至 2003-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0233777&HistoricalAwards=false
• 关键词: Ramsey; Theory; Hypergraph; Coloring; Structural

9970325Professor Mubayi plans to undertake research in graph theory with emphasis on Ramsey theory, hypergraph coloring, connectivity of cages, and graph covering. The main thrust of his project is to study variations of problems in Ramsey Theory posed by Paul Erdos. He will also develop the coloring theory of mixed hypergraphs, investigate the connectivity properties of cages, and study a new problem related to graph covering.The proposed research falls into the general area of combinatorics. One of the goals of combinatorics is to find efficient methods to study arrangements of objects. These methods are extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems or internet providers, deal with finite sets of objects and require combinatorial analysis. Ramsey theory studies the conditions under which certain substructures in a discrete setting are forced to appear. It has applications to efficient information retrieval, to clear communication with noisy channels, and to the effect of failure of intermediate facilities in a communication network.

9970325 Mubayi教授计划进行图论研究，重点是Ramsey理论，超图着色，笼的连通性和图覆盖。他的项目的主旨是研究保罗·鄂尔多斯提出的拉姆齐理论中的问题的变化。他亦会发展混合超图的着色理论，研究笼的连通性，以及研究一个与图覆盖有关的新问题。拟议的研究福尔斯属于组合学的一般领域。组合数学的目标之一是找到有效的方法来研究对象的安排。这些方法对现代通信极为重要。例如，大型网络的设计，如电话系统或互联网提供商中的网络，处理有限的对象集，需要组合分析。 拉姆齐理论研究的条件下，某些子结构在离散设置被迫出现。它可以应用于有效的信息检索，清除有噪声信道的通信，以及通信网络中中间设施故障的影响。