Graph Theory and Combinatorics

图论和组合学

• 批准号: 2763308
• 金额: --
• 依托单位: University of Birmingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2763308
• 关键词: Graph; Theory; Combinatorics

The underlying motto of Ramsey theory is that total disorder is impossible. Ramsey-type theorems also have roots in different branches of mathematics, and the theory developed from them has influenced diverse areas such as number theory, logic, probability theory, geometry and theoretical computer science. Ramsey theory for graphs has a long and rich history with applications in social study, infrastructure, telecommunication and biological networks. This area of research has resulted in development of powerful techniques, such as Szemeredi's regularity lemma and dependent random choice. However, much less is known for Ramsey theory for hypergraphs. For instance the Ramsey number of k-uniform cycles are not known, whereas its graph version is known since the 1970s. The focus of the project is to study question in this area. Another topic of interest will be to classify sparse hypergraphs that has linear Ramsey number.

拉姆齐理论的基本格言是，完全无序是不可能的。拉姆齐型定理也起源于数学的不同分支，从它们发展出来的理论影响了不同的领域，如数论、逻辑、概率论、几何和理论计算机科学。Ramsey图论有着悠久而丰富的历史，在社会研究、基础设施、电信和生物网络中有着广泛的应用。这一领域的研究导致了强大的技术的发展，如Szemeredi的规律性引理和相关随机选择。然而，对于超图的拉姆齐理论知之甚少。例如k-均匀圈的拉姆齐数是未知的，而它的图形版本是自1970年代以来已知的。本项目的重点是研究这一领域的问题。另一个感兴趣的主题将是分类稀疏超图具有线性拉姆齐数。