Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite

Martin Balko, David Chodounský, Jan Hubička, Matěj Konečný, Lluis Vena

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We prove that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. This is the first case where big Ramsey degrees are known to be finite for structures in a non-binary language. Our proof is based on the vector (or product) form of Milliken’s Tree Theorem and demonstrates a general method to carry existing results on structures in binary relational languages to higher arities.

Original languageEnglish
Pages (from-to)659-672
Number of pages14
Issue number5
StatePublished - 1 Oct 2022
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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