Structural problems in random graphs

• Grant number: 20/10796-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2021
• End date: March 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Guilherme Oliveira Mota
• Grantee: José Diego Alvarado Morales
• 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): 22/05307-6 - Ramsey-type problems for graphs and random graphs, BE.EP.PD

Abstract

This project details the research for the postdoctoral position of José Diego Alvarado Morales, which will be developed under the supervision of G. O. Mota at Instituto de Matemática e Estatística, USP, from 01/10/2020 to 30/09/2022. This project focus to achieve significant advances in structural problems for random graphs, as well as the use of random graphs for research problems in Ramsey Theory. Four lines of research will be investigated: orientations of random graphs without aspecific structure, vertex covering of random graphs with monochromatic structures, obtaining rainbow copies of a fixed graph in random graphs, and obtain estimates for the size-Ramsey number of bounded degree graphs. (AU)

Scientific publications

(6)

(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)

ALVARADO, JOSE D.; DE OLIVEIRA, LEONARDO GONCALVES; GRIFFITHS, SIMON. Moderate deviations of triangle counts in sparse Erdős-Rényi random graphs G(n, m) and G(n, p). PROBABILITY THEORY AND RELATED FIELDS, v. N/A, p. 73-pg., 2025-02-19. (20/10796-0)

ALVARADO, JOSE D.; DO COUTO, GABRIEL D.; GRIFFITHS, SIMON R.. MODERATE DEVIATIONS OF TRIANGLE COUNTS - THE LOWER TAIL. PROCEEDINGS OF THE 12TH EUROPEAN CONFERENCE ON COMBINATORICS, GRAPH THEORY AND APPLICATIONS, EUROCOMB 2023, v. N/A, p. 8-pg., 2023-01-01. (20/10796-0)

ALVARADO, JOSE D.; KOHAYAKAWA, YOSHIHARU; MORRIS, PATRICK; MOTA, GUILHERME OLIVEIRA. A canonical Ramsey theorem with list constraints in random graphs. XII LATIN-AMERICAN ALGORITHMS, GRAPHS AND OPTIMIZATION SYMPOSIUM, LAGOS 2023, v. 224, p. 7-pg., 2023-01-01. (18/04876-1, 19/13364-7, 20/10796-0)

ALVARADO, JOSE D.; KOHAYAKAWA, YOSHIHARU; LANG, RICHARD; MOTA, GUILHERME OLIVEIRA; STAGNI, HENRIQUE. Resilience for loose Hamilton cycles. XII LATIN-AMERICAN ALGORITHMS, GRAPHS AND OPTIMIZATION SYMPOSIUM, LAGOS 2023, v. 224, p. 8-pg., 2023-01-01. (18/04876-1, 21/11020-9, 19/13364-7, 20/10796-0)

ALVARADO, JOSE D.; COLUCCILE, LUCAS; PARENTE, ROBERTO; SOUZA, VICTOR. On the Zero-Sum Ramsey Problem over Z₂^d. LATIN 2022: THEORETICAL INFORMATICS, v. 13568, p. 15-pg., 2022-01-01. (20/10796-0, 20/08252-2)

ALVARADO, JOSE D.; DO COUTO, GABRIEL DIAS; GRIFFITHS, SIMON. Moderate deviations of triangle counts in the Erdos-Rényi random graph G(n, m): The lower tail. EUROPEAN JOURNAL OF COMBINATORICS, v. 129, p. 29-pg., 2025-10-01. (20/10796-0)