Banca de DEFESA: URIEL ALEJANDRO SALAZAR MARTÍNEZ

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : URIEL ALEJANDRO SALAZAR MARTÍNEZ
DATE: 19/09/2022
TIME: 10:00
LOCAL: https://meet.google.com/nyj-tnew-wcf
TITLE:

A Study of Probabilistic Versions of Ramsey-Type Properties and Variants

PAGES: 97
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Teoria da Computação
SPECIALTY: Análise de Algoritmos e Complexidade de Computação
SUMMARY:

One of the biggest open problems in Combinatorics
belongs to Ramsey Theory. In this theory, for instance, we
are interested in determining values $n = n(k)$ such that
every $2$-edge coloring of the complete graph $K_{n}$
contains a monochromatic copy of $K_{k}$. A similar
approach, in random graphs, aims to obtain values of $p$ so
that every edge coloring of $G(n,p)$ with $r$ colors
contains a monochromatic copy of a fixed graph $H$. Some
natural generalizations of this theory are the anti-Ramsey
Theory, where we are interested in found a rainbow copy of a
given graph $H$, or we can also combine both the notions
from Ramsey and anti-Ramsey Theory. In Random Graphs there
is a phenomenon, known as threshold, characterized by an
abrupt change, as we vary the value $p$, of the probability
that $G(n,p)$ possesses some property or not. A classic
result from Bollobás and Thomason assures that the
Ramsey-type properties have a threshold, since they belong
to a special type of properties, called increasing
properties. In this work we will study some variants of the
probabilistic versions for the Ramsey, anti-Ramsey and some
generalizations, as well as the progress regarding to
obtaining the thresholds for each of these properties.

BANKING MEMBERS:
Presidente - Interno ao Programa - 663.207.043-49 - GUILHERME OLIVEIRA MOTA - USP
Membro Titular - Examinador(a) Externo à Instituição - ANTONIO JOSEFRAN DE OLIVEIRA BASTOS - UFC
Membro Titular - Examinador(a) Externo à Instituição - ROBERTO FREITAS PARENTE - UFBA
Membro Suplente - Examinador(a) Externo à Instituição - JOSÉ DIEGO ALVARADO MORALES - USP