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)