On 0-1 matrices and small excluded submatrices

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

We say that a 0-1 matrix A avoids another 0-1 matrix (pattern) P if no matrix P′ obtained from P by increasing some of the entries is a submatrix of A. Following the lead of (SIAM J. Discrete Math. 4 (1991) 17-27; J. Combin. Theory Ser. A 55 (1990) 316-320; Discrete Math. 103 (1992) 233-251) and other papers we investigate n by n 0-1 matrices avoiding a pattern P and the maximal number ex (n, P) of 1 entries they can have. Finishing the work of [8] we find the order of magnitude of ex (n, P) for all patterns P with four 1 entries. We also investigate certain collections of excluded patterns. These sets often yield interesting extremal functions different from the functions obtained from any one of the patterns considered.

Original languageEnglish
Pages (from-to)266-288
Number of pages23
JournalJournal of Combinatorial Theory, Series A
Volume111
Issue number2
DOIs
Publication statusPublished - Aug 2005

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(0, 1)-matrices
Extremal Function
P-matrix
Lead

Keywords

  • Extremal problem
  • Forbidden submatrix

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

On 0-1 matrices and small excluded submatrices. / Tardos, G.

In: Journal of Combinatorial Theory, Series A, Vol. 111, No. 2, 08.2005, p. 266-288.

Research output: Contribution to journalArticle

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