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Monochromatic partitions of complete graphs

Grant number: 21/09286-0
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): September 01, 2021
Effective date (End): 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


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)

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