More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

Abstract

In this paper, we compute universal minimal flows of groups of automorphisms of uncountable $\omega$-homogeneous graphs, $K_n$-free graphs, hypergraphs, partially ordered sets, and their extensions with an $\omega$-homogeneous ordering. We present an easy construction of such structures, expanding the jungle of extremely amenable groups.