Year: 2013
Type: preprint
Abstract: Let K_4 denote the complete 3-uniform hypergraph on 4 vertices. Ajtai, Erdős, Komlós, and Szemerédi (1981) asked if there is a function ω(d) tending to infinity such that every 3-uniform, K_4-free hypergraph N vertices and average degree d has independence number at least ω(d) N/d^{1/2}. We answer this question by constructing a 3-uniform, K_4-free hypergraph with independence number at most 2N/d^{1/2}. We also provide counterexamples to several related conjectures and improve the lower bound of some hypergraph Ramsey numbers.
Source: arXiv (Cornell University)
Authors: Cooper, Jeff, Mubayi, Dhruv
Institution: University of Illinois Chicago
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2952147640