Big Ramsey degrees of 3-uniform hypergraphs are finite
Combinatorics
2021-07-06 v3 Discrete Mathematics
Logic
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.
Keywords
Cite
@article{arxiv.2008.00268,
title = {Big Ramsey degrees of 3-uniform hypergraphs are finite},
author = {Martin Balko and David Chodounský and Jan Hubička and Matěj Konečný and Lluis Vena},
journal= {arXiv preprint arXiv:2008.00268},
year = {2021}
}
Comments
10 pages, 2 figures. Minor corrections and presentation improvements suggested by the referees