Off-diagonal Ramsey numbers for linear hypergraphs
Abstract
Abstract We study off-diagonal Ramsey numbers r left parenthesis upper H comma upper K Subscript n Superscript left parenthesis k right parenthesis Baseline right parenthesis r ( H , K n ( k ) ) $r(H, K_n^{(k)})$ of k k $k$ -uniform hypergraphs, where upper H H $H$ is a fixed linear k k $k$ -uniform hypergraph and upper K Subscript n Superscript left parenthesis k right parenthesis K n ( k ) $K_n^{(k)}$ is complete on n n $n$ vertices. Recently, Conlon, Fox, Gunby, He, Mubayi, Suk, and Verstraëte disproved the folklore conjecture that r left parenthesis upper H comma upper K Subscript n Superscript left parenthesis 3 right parenthesis Baseline right parenthesis r ( H , K n ( 3 ) ) $r(H, K_n^{(3)})$ always grows polynomially in n
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Topology and Set Theory
Advanced Graph Theory Research
Publication details
- Journal / source
- Combinatorics Probability Computing
- Publisher
- Cambridge University Press (CUP)
- Volume
- 35
- Issue
- 4
- Pages
- 554–567
- Publication date
- 14 April 2026
- Language
- EN