Big ramsey degrees of 3-uniform hypergraphs

M. Balko, D. Chodounský, J. Hubička, M. Konečný, L. Vena

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Given a countably infinite hypergraph R and affnite hypergraph A, the big Ramsey degree of A in R is the least number L such that, for every finite k and every k-colouring of the embeddings of A to R, there exists an embedding f from R to R such that all the embeddings of A to the image f(R) have at most L different colours. We describe the big Ramsey degrees of the random countably infinite 3-uniform hypergraph, thereby solving a question of Sauer. We also give a new presentation of the results of Devlin and Sauer on, respectively, big Ramsey degrees of the order of the rationals and the countably infinite random graph. Our techniques generalise (in a natural way) to relational structures and give new examples of Ramsey structures (a concept recently introduced by Zucker with applications to topological dynamics).

Original languageEnglish
Pages (from-to)415-422
Number of pages8
JournalActa Mathematica Universitatis Comenianae
Issue number3
StatePublished - 2 Sep 2019
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)


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