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On minimum saturated matrices
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Dudek, Andrzej, Pikhurko, Oleg and Thomason, Andrew (2013) On minimum saturated matrices. Graphs and Combinatorics, Volume 29 (Number 5). pp. 1269-1286. doi:10.1007/s00373-012-1199-2 ISSN 0911-0119.
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Official URL: http://dx.doi.org/10.1007/s00373-012-1199-2
Abstract
Motivated both by the work of Anstee, Griggs, and Sali on forbidden submatrices and also by 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 F∈F (as a row and column permutation of F). 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 minimal number of columns of an F -saturated matrix with n rows. We establish the estimate sat (n,F)=O(nk−1) for any family F of k-row matrices and also compute the sat-function for a few small forbidden matrices.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Graphs and Combinatorics | ||||
Publisher: | Springer Japan KK | ||||
ISSN: | 0911-0119 | ||||
Official Date: | September 2013 | ||||
Dates: |
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Volume: | Volume 29 | ||||
Number: | Number 5 | ||||
Page Range: | pp. 1269-1286 | ||||
DOI: | 10.1007/s00373-012-1199-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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