
Navid Talebanfard
 (IM CAS)

Random 3regular graphs from random 3regular graphs

Abstract:

Given a 3regular graph we define a natural process which gives a random topological minor of this graph. We
show that if the original graph is uniformly distributed, so is the resulting topological minor over the
space of 3regular graphs of the same size.
Based on ongoing work with Pavel Pudlák and Neil Thapen.

Jan Hladký
 (IM CAS)

Graphons as weak* limits

Abstract:

Around 2004, Lovasz and Szegedy came up with a certain compactification of the space of finite graphs.
More precisely, they proved that there exists a metric  now called the cutdistance  which yields a
compact topology. Their proof of compactnes relies on the Szemeredi regularity lemma. An entire theory,
with applications in extremal graph theory and random graphs, developed from this statement. I will
talk about approaching the cutnorm topology via the weak* topology. This approach gives a new view of
many properties, and in particular yields a quick and elementary proof of the LovaszSzegedy theorem.
The talk will be selfcontained. Various bits of this are joint work with Martin Dolezal, Jan Grebik,
Jon Noel, Diana Piguet, Israel Rocha, Vaclav Rozhon, Maria Saumell.
Michal Koucky, Pavel Pudlak
organizers