DATE: 25 November 2020

SPEAKER: Alberto Espuny Díaz (https://sites.google.com/view/alberto-espuny-diaz/)

TITLE: Perturbing graphs by a random regular graph: Hamiltonicity and pancyclicity

ABSTRACT: The study of randomly perturbed graphs has received a lot of
attention in recent years. In this area, we consider the union of a dense
deterministic graph $H$ (usually with some minimum degree condition) and a
random graph $G$, and the main goal is to improve threshold results for random
graphs by considering the union with $H$: there are many results showing that,
in order for $H\cup G_{n,p}$ to satisfy a given property $\mathcal{P}$, the
minimum $p$ which is required is substantially smaller than that required for
$G_{n,p}$ itself.

In this talk, I will introduce the model of randomly perturbed graphs and some
of the results that have been obtained so far, and then I will present some new
results about Hamiltonicity and pancyclicity when we let $G$ be a random
regular graph. This is joint work with António Girão.