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Threshold functions for anti-Ramsey properties

Grant number: 19/15048-5
Support type:Scholarships in Brazil - Master
Effective date (Start): October 01, 2019
Effective date (End): September 30, 2021
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Computational Mathematics
Principal Investigator:Guilherme Oliveira Mota
Grantee:Uriel Alejandro Salazar Martínez
Home Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
Associated research grant:18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics, AP.JP

Abstract

Given an edge-coloring of the edges of a graph G, we say that a copy of H in G is rainbow if there are no two edges of H with the same color. In this project we are interested in making an advanced study and obtain advances on the investigation of the following graph property, known as anti-Ramsey property: for any coloring of the edges of G there exists a rainbow copy of H in G, i.e., a copy of H such that there are no two edges with the same color. We denote this property by G-> H. We will study recent results that describe the threshold function for the anti-Ramsey property G(n,p)-> H for some fixed graphs H. In the second part of this project we will try to apply modern combinatorial techniques to get good bounds for the threshold of the property G(n,p)-> H for some graph classes H. (AU)