DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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DMTCS Conference vol AE (2005), pp. 77-80

DMTCS

2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 77-80


author: John Talbot
title: Chromatic Turán problems and a new upper bound for the Turán density of
K
4
-
keywords: Extremal combinatorics, Turán-type problems, Hypergraphs
abstract: We consider a new type of extremal hypergraph problem: given an
r
-graph
F
and an integer
k≥2
determine the maximum number of edges in an
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
33 / 100
, improving previous bounds of
1 / 3
due to de Caen [deC], and
1 / 3-4.5305×10
-6
due to Mubayi [M].
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reference: John Talbot (2005), Chromatic Turán problems and a new upper bound for the Turán density of
K
4
-
, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 77-80
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