Color critical hypergraphs and forbidden configurations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2005

Color critical hypergraphs and forbidden configurations


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.
Fichier principal
Vignette du fichier
dmAE0123.pdf (157.79 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-01184389 , version 1 (14-08-2015)



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, ⟨10.46298/dmtcs.3432⟩. ⟨hal-01184389⟩


98 View
498 Download



Gmail Facebook Twitter LinkedIn More