Monochromatic partitions of complete graphs

• Grant number: 21/09286-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2021
• End date: August 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Theory of Computation
• Principal Investigator: Guilherme Oliveira Mota
• Grantee: André Yuji Hisatsuga
• 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

Abstract

Problems in Ramsey Theory related to partitioning the set of vertices of a graph $G$ into monochromatic structures (given a certain coloring of the edges of the graph) have always intrigued researchers in the field. Recently, several advances have been obtained through the use of different techniques (old and modern).In this project, we plan for the student to study in detail the articles that led to the definitive solution of the problem of partitioning all complete graphs whose edges are colored into monochromatic cycles. This will lead the student to understand in detail some of the techniques usually applied in Ramsey Theory. Finally, the student will study a recent work by Grinshpun and Sárközy that deals with a generalization of the problem of partitioning complete graphs into monochromatic cycles.(AU)