Carnegie Mellon University
Browse

Turán Densities of Some Hypergraphs Related to K_{k+1}^{k}

Download (151.33 kB)
journal contribution
posted on 2012-09-12, 00:00 authored by József Balogh, Tom Bohman, Béla Bollobás, Yi Zhao

Let $B_i^{(k)}$ be the $k$-uniform hypergraph whose vertex set is of the form $S\cup T$, where $|S|=i$, $|T|=k-1$, and $S\cap T=\emptyset$, and whose edges are the $k$-subsets of $S\cup T$ that contain either $S$ or $T$. We derive upper and lower bounds for the Turán density of $B_i^{(k)}$ that are close to each other as $k\to\infty$. We also obtain asymptotically tight bounds for the Turán density of several other infinite families of hypergraphs. The constructions that imply the lower bounds are derived from elementary number theory by probabilistic arguments, and the upper bounds follow from some results of de Caen, Sidorenko, and Keevash.

History

Publisher Statement

© 2012, Society for Industrial and Applied Mathematics

Date

2012-09-12

Usage metrics

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC