Department of
Applied
Mathematics

Jirka Matoušek Prize Noon lecture: Structural Ramsey theory, homomorphism dualities and completions

Matěj Konečný

KAM MFF Charles University

Abstract

In this lecture, we review our current understanding of the interplay of the Ramsey property (and other combinatorial properties of classes of structures such as the extension property for partial automorphisms) and (restricted) homomorphism dualities for classes of edge-labelled graphs. This is done via the concept of completions introduced by Hubička and Nešetřil. We will see both general theorems and specific applications (e.g. Cherlin's classes of metrically homogeneous graphs).