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

Access to Document

10.1007/s00493-021-4664-9

Cite this

@article{71f07cec2c714245b2aa225ded078d38,

title = "Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite",

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{\textquoteright}s Tree Theorem and demonstrates a general method to carry existing results on structures in binary relational languages to higher arities.",

author = "Martin Balko and David Chodounsk{\'y} and Jan Hubi{\v c}ka and Mat{\v e}j Kone{\v c}n{\'y} and Lluis Vena",

note = "Publisher Copyright: {\textcopyright} 2022, J{\'a}nos Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.",

year = "2022",

month = oct,

day = "1",

doi = "10.1007/s00493-021-4664-9",

language = "English",

volume = "42",

pages = "659--672",

journal = "Combinatorica",

issn = "0209-9683",

publisher = "Janos Bolyai Mathematical Society",

number = "5",

}

TY - JOUR

T1 - Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite

AU - Balko, Martin

AU - Chodounský, David

AU - Hubička, Jan

AU - Konečný, Matěj

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.

UR - http://www.scopus.com/inward/record.url?scp=85124740484&partnerID=8YFLogxK

U2 - 10.1007/s00493-021-4664-9

DO - 10.1007/s00493-021-4664-9

M3 - Article

AN - SCOPUS:85124740484

SN - 0209-9683

VL - 42

SP - 659

EP - 672

JO - Combinatorica

JF - Combinatorica

IS - 5

ER -

Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this