Problems in Ramsey Theory, random graphs and embeddings

• Grant number: 19/04375-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2019
• End date: May 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Yoshiharu Kohayakawa
• Grantee: Tássio Naia dos Santos
• 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
• Associated scholarship(s): 20/16570-4 - Problems in Ramsey Theory, random graphs and embeddings, BE.EP.PD

Abstract

This is the research proposal for the post-doctoral fellowship of Tássio Naia dos Santos, to be pursued under the supervision of Yoshiharu Kohayakawa, at the Instituto de Matemática e Estatística, Universidade de São Paulo, from 1/5/2019 to 31/4/2021. This proposal is focused on attaining significant advances in several problems in extremal and probabilistic combinatorics. This includes the following main themes (a) embedding of spanning oriented graphs in digraphs; (b) Ramsey Theory; and (c) probabilistic graph theory. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

NAIA, TASSIO. Trees contained in every orientation of a graph. ELECTRONIC JOURNAL OF COMBINATORICS, v. 29, n. 2, p. 5-pg., 2022-05-06. (19/04375-5, 18/04876-1, 19/13364-7)

BOTLER, FABIO; MOURA, PHABLO F. S.; NAIA, TASSIO. Seymour's Second Neighborhood Conjecture for orientations of (pseudo)random graphs. DISCRETE MATHEMATICS, v. 346, n. 12, p. 12-pg., 2023-12-01. (20/16570-4, 19/04375-5, 19/13364-7)