[Settfa] Tuesday 3 June, Andrés Aranda

[David Bradley-Williams]

Tuesday, 3 June 2025 - 10:00 to 11:30
Place: IM, konírna

Speaker: Andrés Aranda
Title: Constructing HH-homogeneous graphs from finite reflexive 
templates

Abstract

Few explicit constructions of HH-homogeneous exist in the literature. We 
do have a Fraïssé theorem for homomorphism-homogeneous structures, but 
finding amalgamation classes that produce interesting graphs is hard. 
Here, ``interesting'' means that some finite subset of vertices is not 
dominated by a single vertex.

The few examples known are the simplest possible graphs in the class, 
which leaves many questions unanswered. In this talk, I will present a 
new form of homogeneity and show that finite reflexive graphs that 
satisfy it can be used as templates for countably infinite 
homomorphism-homogeneous graphs. The construction produces new examples 
and helps clarify the connection between finite graphs and countably 
infinite homomorphism-homogeneous graphs.

This is joint work with D. Bradley-Williams and D. Hartman.

For more information see the seminar web page at
https://www.math.cas.cz/index.php/events/seminar/6

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