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arXiv · 0909.1970

On Minimum Saturated Matrices

Andrzej Dudek·Oleg Pikhurko·Andrew Thomason
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Abstract

Motivated by the work of Anstee, Griggs, and Sali on forbidden submatrices and the extremal sat-function for graphs, we introduce sat-type problems for matrices. Let F be a family of k-row matrices. A matrix M is called F-admissible if M contains no submatrix G\in F (as a row and column permutation of G). A matrix M without repeated columns is F-saturated if M is F-admissible but the addition of any column not present in M violates this property. In this paper we consider the function sat(n,F) which is the minimum number of columns of an F-saturated matrix with n rows. We establish the estimate sat(n,F)=O(n^{k-1}) for any family F of k-row matrices and also compute the sat-function for a few small forbidden matrices.

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Andrzej Dudek, Oleg Pikhurko, Andrew Thomason. 2012-05-24. On Minimum Saturated Matrices. https://arxiv.org/abs/0909.1970

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