Flows of linear orders on sparse graphs

Abstract: We consider the topological dynamics of the automorphism group of a particular sparse graph M_1 resulting from an ab initio Hrushovski construction. We show that minimal subflows of the flow of linear orders on M_1 have all orbits meagre, partially answering a question of Tsankov regarding results of Evans, Hubicka and Nesetril on the topological dynamics of automorphism groups of sparse graphs.