DeepAI AI Chat
Log In Sign Up

Big Ramsey degrees of 3-uniform hypergraphs

by   Martin Balko, et al.
Akademie věd ČR
Charles University in Prague

Given a countably infinite hypergraph R and a finite 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).


page 1

page 2

page 3

page 4


Big Ramsey degrees of 3-uniform hypergraphs are finite

We prove that the universal homogeneous 3-uniform hypergraph has finite ...

Big Ramsey degrees and infinite languages

This paper investigates big Ramsey degrees of unrestricted relational st...

Big Ramsey degrees and forbidden cycles

Using the Carlson-Simpson theorem, we give a new general condition for a...

Finite Atomized Semilattices

We show that every finite semilattice can be represented as an atomized ...

Sampling hypergraphs with given degrees

There is a well-known connection between hypergraphs and bipartite graph...

Learning Non-Uniform Hypergraph for Multi-Object Tracking

The majority of Multi-Object Tracking (MOT) algorithms based on the trac...

Characterisation of the big Ramsey degrees of the generic partial order

As a result of 33 intercontinental Zoom calls, we characterise big Ramse...