# 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.
Keywords :
Type de document :
Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.117-122, 2005, DMTCS Proceedings
Domaine :
Liste complète des métadonnées

Littérature citée [9 références]

https://hal.inria.fr/hal-01184389
Contributeur : Coordination Episciences Iam <>
Soumis le : vendredi 14 août 2015 - 11:39:09
Dernière modification le : jeudi 11 mai 2017 - 01:02:52
Document(s) archivé(s) le : dimanche 15 novembre 2015 - 11:05:59

### Fichier

dmAE0123.pdf
Fichiers éditeurs autorisés sur une archive ouverte

### Identifiants

• HAL Id : hal-01184389, version 1

### Citation

Richard Anstee, Balin Fleming, Zoltán Füredi, Attila Sali. Color critical hypergraphs and forbidden configurations. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.117-122, 2005, DMTCS Proceedings. 〈hal-01184389〉

### Métriques

Consultations de la notice

## 112

Téléchargements de fichiers