Extremal and Structural Problems in Graph Theory

Abstract

This is a research project for the joint call of proposals between the São Paulo Research Foundation (FAPESP), Brazil, and the Comisión Nacional de Investigación Científica y Tecnológica (CONICYT), Chile. The Brazilian and the Chilean teams have been working in Combinatorics and Graph Theory for several years now. Some of the Brazilian members have already collaborated with some of the Chilean members of the team.This joint application intends to establish and consolidate a cooperation between both teams by working collaboratively on important problems in the areas.The lines of research proposed in this project belong to the field of graph theory and its variants.Graphs are mathematical structures that have applications in a variety of subjects and real-world problems, ranging from computer science over physics to social networks.Our main objective is to study graphs from a theoretical point of view, thus contributing to a better understanding of the laws that govern the behavior of these structures.Progress in this objective should provide new strategies for related problems, as well as make available new techniques for problems in several areas of knowledge.A study of various combinatorial techniques and a good understanding of structural properties of graphs are the pillars of this project, which should lead to the solutions of relevant open problems. The present project will also contribute to the strengthening of the national and international insertion of the involved universities. We remark that the proposed teams contain a mix of young academics with outstanding academic performance and renowned researchers who have extensive experience in the problems to be investigated. (AU)