Structural and extremal properties of graphs and hypergraphs

• Grant number: 20/03336-3
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2021
• End date: March 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Guilherme Oliveira Mota
• Grantee: Pedro Santos Mota e Arraes
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics, AP.JP

Abstract

This project focuses on the study of Ramsey, anti-Ramsey and size-Ramsey properties of random and deterministic graphs. In this project we plan to investigate three research lines on Extremal Combinatorics: graph decomposition, pseudorandom structures, and the study of extreme properties on dense and sparse graphs. Problems on these lines have been recieving plenty of attention by researchers these last few years, where new results were obtained due to the development of powerfull techniques related to the regularity method, the hypergraph containers method, amongst others. (AU)