## DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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DMTCS Conference vol AE (2005), pp. 117-122

## 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

### DMTCS Conference Volume AE (2005), pp. 117-122

author: Richard Anstee, Balin Fleming, Zoltán Füredi and Attila Sali Color critical hypergraphs and forbidden configurations forbidden configuration, color critical hypergraph, linear algebra method 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) 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. If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. 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. 117-122 For a corresponding BibTeX entry, please consider our BibTeX-file. dmAE0123.ps.gz (71 K) dmAE0123.ps (169 K) dmAE0123.pdf (157 K)