Hypergraph Ramsey numbers of cliques versus stars-Reference-Cited by-同舟云学术

Hypergraph Ramsey numbers of cliques versus stars

Published:2023-05-18 Issue:3 Volume:63 Page:610-623
ISSN:1042-9832
Container-title:Random Structures & Algorithms
language:en
Short-container-title:Random Struct Algorithms

Author:

Conlon David¹,Fox Jacob²,He Xiaoyu³^ORCID,Mubayi Dhruv⁴,Suk Andrew⁵,Verstraëte Jacques⁵

Affiliation:

1. Department of Mathematics California Institute of Technology Pasadena California USA

2. Department of Mathematics Stanford University Stanford California USA

3. Department of Mathematics Princeton University Princeton New Jersey USA

4. Department of Mathematics, Statistics and Computer Science University of Illinois Chicago Illinois USA

5. Department of Mathematics University of California at San Diego La Jolla California USA

Abstract

AbstractLet denote the complete 3‐uniform hypergraph on vertices and the 3‐uniform hypergraph on vertices consisting of all edges incident to a given vertex. Whereas many hypergraph Ramsey numbers grow either at most polynomially or at least exponentially, we show that the off‐diagonal Ramsey number exhibits an unusual intermediate growth rate, namely, for some positive constants and . The proof of these bounds brings in a novel Ramsey problem on grid graphs which may be of independent interest: what is the minimum such that any 2‐edge‐coloring of the Cartesian product contains either a red rectangle or a blue ?

Publisher

Wiley

Subject

Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/rsa.21155

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