Abstract
This project describes the research to be carried out at the Instituto de Matemática e Estatística (IME-USP) by the researcher Walner Mendonça (PhD in Mathematics from IMPA) and his supervisor Guilherme O. Mota, in the period from 09/01/2023 to 08/31/2025.Part of this project is dedicated to the study of monochromatic tilings and covers problems in complete graphs and in random graphs. We…