Year: 2012
Type: preprint
Abstract: The Turán density π(H) of a family H of k-graphs is the limit as n tends to infinity of the maximum edge density of an H-free k-graph on n vertices. Let I^k consist of all possible Turán densities and let F^k be the set of Turán densities of finite k-graph families. Here we prove that F^k contains every density obtained from an arbitrary finite construction by optimally blowing it up and using recursion inside the specified set of parts. As an application, we show that F^k contains an irrational number for each k\ge 3. Also, we show that I^k has cardinality of the continuum. In particular, I^k is not equal to F^k.
Source: arXiv (Cornell University)
Author: Pikhurko, Oleg
Institution: University of Warwick
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2949177194