Extremal hypergraph problems

1979 ◽  
pp. 44-65 ◽  
Author(s):  
D.J. Kleitman
Keyword(s):  
Extremal Hypergraph

Density theorems and extremal hypergraph problems

2006 ◽  
Vol 152 (1) ◽  
pp. 371-380 ◽  
Author(s):  
V. Rödl ◽  
E. Tengan ◽  
M. Schacht ◽  
N. Tokushige
Keyword(s):  
Density Theorems ◽  
Extremal Hypergraph

New Turán Exponents for Two Extremal Hypergraph Problems

2020 ◽  
Vol 34 (4) ◽  
pp. 2338-2345
Author(s):  
Chong Shangguan ◽  
Itzhak Tamo
Keyword(s):  
Extremal Hypergraph

scholarly journals Chromatic Turán problems and a new upper bound for the Turán density of $\mathcal{K}_4^-$

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
John Talbot
Keyword(s):  
Upper Bound ◽  
Turan Problems ◽  
International Audience ◽  
New Type ◽  
Extremal Hypergraph

International audience We consider a new type of extremal hypergraph problem: given an $r$-graph $\mathcal{F}$ and an integer $k≥2$ determine the maximum number of edges in an $\mathcal{F}$-free, $k$-colourable $r$-graph on $n$ vertices. Our motivation for studying such problems is that it allows us to give a new upper bound for an old problem due to Turán. We show that a 3-graph in which any four vertices span at most two edges has density less than $\frac{33}{ 100}$, improving previous bounds of $\frac{1}{ 3}$ due to de Caen [1], and $\frac{1}{ 3}-4.5305×10^-6$ due to Mubayi [9].

Extremal Hypergraph Problems and the Regularity Method

2007 ◽  
pp. 247-278 ◽  
Author(s):  
Brendan Nagle ◽  
Vojtěch Rödl ◽  
Mathias Schacht
Keyword(s):  
Extremal Hypergraph

scholarly journals On An Extremal Hypergraph Problem Of Brown, Erdős And Sós

COMBINATORICA ◽  
2006 ◽  
Vol 26 (6) ◽  
pp. 627-645 ◽  
Author(s):  
Noga Alon* ◽  
Asaf Shapira†
Keyword(s):  
Extremal Hypergraph

scholarly journals On an extremal hypergraph problem related to combinatorial batch codes

2014 ◽  
Vol 162 ◽  
pp. 373-380 ◽  
Author(s):  
Niranjan Balachandran ◽  
Srimanta Bhattacharya
Keyword(s):  
Extremal Hypergraph

scholarly journals Constructions of non-principal families in extremal hypergraph theory

2008 ◽  
Vol 308 (19) ◽  
pp. 4430-4434 ◽  
Author(s):  
Dhruv Mubayi ◽  
Oleg Pikhurko
Keyword(s):  
Extremal Hypergraph ◽  
Hypergraph Theory

scholarly journals Extremal Hypergraphs for the Biased Erdős-Selfridge Theorem

10.37236/2394 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Eric Lars Sundberg
Keyword(s):  
Winning Strategy ◽  
Simple Criterion ◽  
Uniform Hypergraphs ◽  
Positional Games ◽  
Extremal Hypergraph

A positional game is essentially a generalization of Tic-Tac-Toe played on a hypergraph $(V,{\cal F}).$  A pivotal result in the study of positional games is the Erdős–Selfridge theorem, which gives a simple criterion for the existence of a Breaker's winning strategy on a finite hypergraph ${\cal F}$.  It has been shown that the bound in the Erdős–Selfridge theorem can be tight and that numerous extremal hypergraphs exist that demonstrate the tightness of the bound. We focus on a generalization of the Erdős–Selfridge theorem proven by Beck for biased $(p:q)$ games, which we call the $(p:q)$–Erdős–Selfridge theorem.  We show that for $pn$-uniform hypergraphs there is a unique extremal hypergraph for the $(p:q)$–Erdős–Selfridge theorem when $q\geq 2$.

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