Modern techniques in extremal combinatorics

• Grant number: 25/07650-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2025
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Theory of Computation
• Principal Investigator: Guilherme Oliveira Mota
• Grantee: Bryan Barros de Lima
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 24/13859-4 - Ramsey Theory: from monochromatic to canonical structures, AP.R

Abstract

In May 2022, Glock, Joos, Kim, Kühn, and Lichev[Conflict-free hypergraph matchings, Proceedings of the 2023Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2023) -2991-3005] developed a strategy to find near-perfect matchings in uniform hypergraphs while avoiding certain subsets. This work was very recently extended by Joos, Mubayi, and Smith [Conflict-free Hypergraph Matchings and Coverings, https://arxiv.org/abs/2407.18144], who established methods to find perfect matchings covering a given set of vertices, thus broadening the applicability of the technique. We propose a detailed study of one of these works. (AU)