Dissertação de Mestrado Acadêmico - Bruno Baldissera Carlotto

Title: Connectivity of Friends and Strangers graphs 

Abstract: One of the central problems studied in probabilistic combinatorics is determining thresholds for properties in random graphs. In this dissertation, we determine, up to a constant factor, the connectivity threshold of the Friends-and-strangers graph FS(G,H) in the random setting, where G and H are independent Erdős-Rényi random graphs.

We also discuss thresholds for connectivity properties of Erdős-Rényi random graphs G(n,p) and graph packings. In particular, we present a result by Bollobás, Janson and Scott in which they locate up to a constant factor the threshold for the existence of a packing between two independent random graphs G(n,p) and G(n,q).

Banca Examinadora: 
Orientador: Simon Griffiths - PUC-Rio
Marcelo Soares Campos - IMPA
Lucas Souza Mota de Aragão - UFRJ
Luiz Paulo Freire Moreira - UFPE
Grigory Ivanov - PUC-Rio
Suplente: Rodrigo Bezerra de Matos - PUC-Rio

Data: 17 de abril de 2026
Horário: 10h 30min
Sala: L856