Skip to Main content Skip to Navigation
Conference papers

Color critical hypergraphs and forbidden configurations

Abstract : The present paper connects sharpenings of Sauer's bound on forbidden configurations with color critical hypergraphs. We define a matrix to be \emphsimple 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 $forb(m,F)$ as the best possible upper bound on n, for such a matrix $A$, which depends on m and $F$. It is known that $forb(m,F)=O(m^k)$ for any $F$, and Sauer's bond states that $forb(m,F)=O(m^k-1)$ fore simple $F$. We give sufficient condition for non-simple $F$ to have the same bound using linear algebra methods to prove a generalization of a result of Lovász on color critical hypergraphs.
Complete list of metadata

Cited literature [9 references]  Display  Hide  Download

https://hal.inria.fr/hal-01184389
Contributor : Coordination Episciences Iam <>
Submitted on : Friday, August 14, 2015 - 11:39:09 AM
Last modification on : Friday, December 18, 2020 - 5:30:06 PM
Long-term archiving on: : Sunday, November 15, 2015 - 11:05:59 AM

File

dmAE0123.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01184389, version 1

Collections

Citation

Richard Anstee, Balin Fleming, Zoltán Füredi, Attila Sali. Color critical hypergraphs and forbidden configurations. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.117-122. ⟨hal-01184389⟩

Share

Metrics

Record views

197

Files downloads

1022