Ramsey Precompact Expansions of Homogeneous Directed Graphs


In 2005, Kechris, Pestov and Todorčević provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow, immediately leading to an explicit representation of this invariant in many concrete cases. More recently, the framework was generalized allowing for further applications, and the purpose of this paper is to apply these new methods in the context of homogeneous directed graphs. In this paper, we show that the age of any homogeneous directed graph allows a Ramsey precompact expansion. Moreover, we verify the relative expansion properties and consequently describe the respective universal minimal flows.

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@article{Jasinski2014RamseyPE, title={Ramsey Precompact Expansions of Homogeneous Directed Graphs}, author={Jakub Jasinski and Claude Laflamme and Lionel Nguyen Van Th{\'e} and Robert E. Woodrow}, journal={Electr. J. Comb.}, year={2014}, volume={21}, pages={P4.42} }