2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 7780
author:  John Talbot 

title: 
Chromatic Turán problems and a new upper bound for
the Turán density of
K
4


keywords:  Extremal combinatorics, Turántype problems, Hypergraphs 
abstract: 
We consider a new type of extremal hypergraph problem:
given an
r
graph
F
k≥2
determine the maximum number of edges in an
F
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
33 / 100
, improving previous bounds of
1 / 3
due to de Caen [deC], and
1 / 34.5305×10
due to Mubayi [M].
6

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reference: 
John Talbot (2005), Chromatic Turán problems and a
new upper bound for the Turán density of
K
, in 2005 European Conference on Combinatorics,
Graph Theory and Applications (EuroComb '05), Stefan
Felsner (ed.), Discrete Mathematics and Theoretical
Computer Science Proceedings AE, pp. 7780
4


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