Threshold functions for anti-Ramsey properties

• Grant number: 19/15048-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: October 01, 2019
• End date: December 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Guilherme Oliveira Mota
• Grantee: Uriel Alejandro Salazar Martínez
• Host 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)