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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2005

Color critical hypergraphs and forbidden configurations

Résumé

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.
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Dates et versions

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

Identifiants

Citer

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⟩

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