Large substructures in hypergraphs

超图中的大型子结构

• 批准号: 450397222
• 负责人: Dr. Richard Lang
• 金额: --
• 依托单位: Arbeitsgruppe Theoretische Informatik
• 依托单位国家: 德国
• 项目类别: WBP Position
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/450397222?language=en
• 关键词: Large; substructures; hypergraphs

An important question in modern graph theory is whether a given graph contains certain large substructures such as perfect matchings or Hamilton cycles. This project seeks to advance our understanding of these problems in the setting of hypergraphs. The proposed research considers a series of open questions concerning minimum degree conditions and Ramsey numbers of tight cycles, paths and trees in hypergraphs. To solve these problems, new techniques based on hypergraph regularity and the absorption method will be developed, which could be of independent interest.

现代图论中的一个重要问题是给定的图是否包含某些大子结构，如完美匹配或汉密尔顿圈。这个项目旨在推进我们对超图设置中这些问题的理解。研究了超图中紧圈、紧路和紧树的最小度条件和Ramsey数。为了解决这些问题，将开发基于超图正则性和吸收方法的新技术，这可能是独立的兴趣。