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Ramsey and anti-Ramsey structures in deterministic and random graphs

Grant number: 18/22768-1
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2019
Effective date (End): February 28, 2022
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Computational Mathematics
Principal Investigator:Guilherme Oliveira Mota
Grantee:Paulo Matias da Silva Junior
Home Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
Associated research grant:18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics, AP.JP

Abstract

This is the project for the PhD of Paulo Matias da Silva Junior supervised by Professor Guilherme Oliveira Mota, at the Centro de Matemática, Computação e Cognição, UFABC, from 11/2/2019 to 10/8/2022 (3 and a half years, including an internship of six months abroad). This project focuses on the study of Ramsey, anti-Ramsey and size-Ramsey properties of random and deterministic graphs. The problems proposed here will be investigated through classical techniques such as the Szemerédi Regularity Lemma and their variants, and modern techniques such as the method of Hypergraphs Containers. We estimate that this PhD project will be completed within the proposed deadline because of the academic knowledge of the candidate and the experience of the advisor in the area. The starting point of the project will be the study of works by Erdos, Kohayakawa, Rödl, Sárközy, Szemerédi, among others, besides the works of the advisor. At the end of this project, the candidate will have a substantial experience in combinatorics and will have contributed with the scientific development of the area through original research works.During the execution of the project the candidate will benefit from contact with renowned researchers from Brazil and abroad who will visit UFABC. Several of these visits are already scheduled and will occur over the next four years, with resources of the Jovens Pesquisadores em Centro Emergente - Process number 2018/04876-1 - coordinated by the advisor. (AU)