Counting big Ramsey degrees of the homogeneous and universal K4-free graph
Abstract
Big Ramsey degrees of Fra\"iss\'e limits of finitely constrained free amalgamation classes in finite binary languages have been recently fully characterised by Balko, Chodounsk\'y, Dobrinen, Hubicka, Konecn\'y, Vena, and Zucker. A special case of this characterisation is the universal homogeneous K4-free graph. We give a self-contained and relatively compact presentation of this case and compute the actual big Ramsey degrees of small graphs.
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