Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite

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

doi:10.1007/s00493-021-4664-9

Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite

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

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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 language	English
Pages (from-to)	659-672
Number of pages	14
Journal	Combinatorica
Volume	42
Issue number	5
DOIs	https://doi.org/10.1007/s00493-021-4664-9
State	Published - 1 Oct 2022
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-021-4664-9

Cite this

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AU - Vena, Lluis

PY - 2022/10/1

Y1 - 2022/10/1

N2 - 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.

AB - 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.

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Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite

Abstract

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