2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 117122
author:  Richard Anstee, Balin Fleming, Zoltán Füredi and Attila Sali 

title:  Color critical hypergraphs and forbidden configurations 
keywords:  forbidden configuration, color critical hypergraph, linear algebra method 
abstract: 
The present paper connects sharpenings of Sauer's bound on
forbidden configurations with color critical hypergraphs.
We define a matrix to be simple if it is a
(0,1)matrix with no repeated columns. Let
F
be a
k× l
(0,1)matrix (the forbidden configuration). Assume
A
is an
m× n
simple matrix which has no submatrix which is a row
and column permutation of
F
. We define
forb
(m,F)
n
, for such a matrix
A
, which depends on
m
and
F
. It is known that
forb
(m,F)=O(m
k
)
F
, and Sauer's bond states that
forb
(m,F)=O(m
k1
)
F
. We give sufficient condition for nonsimple
F
to have the same bound using linear algebra methods
to prove a generalization of a result of Lovász on
color critical hypergraphs.

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reference:  Richard Anstee and Balin Fleming and Zoltán Füredi and Attila Sali (2005), Color critical hypergraphs and forbidden configurations, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 117122 
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