Large substructures in hypergraphs

现代图论中的一个重要问题是，给定的图是否包含某些大的子结构，如完美匹配或哈密尔顿圈。这个项目试图促进我们对超图设置中的这些问题的理解。所提出的研究考虑了一系列关于超图中紧圈、路和树的最小度条件和Ramsey数的公开问题。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，这可能是独立感兴趣的。

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.