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math.CO2025
Counting big Ramsey degrees of the homogeneous and universal -free graph
Jan Hubička, Matěj Konečný, Štěpán Vodseďálek +1
Big Ramsey degrees of Fraïssé limits of finitely constrained free amalgamation classes in finite binary languages have been recently fully characterised by Balko, Chodounský, Dobri…
math.CO2025
On Big Ramsey degrees of universal -edge-labeled hypergraphs
Jan Hubička, Matěj Konečný, Stevo Todorcevic +1
We show that the big Ramsey degrees of every countable universal -uniform -edge-labeled hypergraph are infinite for every . Together with a recent result of Braunfel…
math.CO2025
Twenty years of Nešetřil's classification programme of Ramsey classes
Jan Hubička, Matěj Konečný
In the 1970s, structural Ramsey theory emerged as a new branch of combinatorics. This development came with the isolation of the concepts of the -Ramsey property and Ra…