Representations of families of triples over GF(2)

Z. Füredi, Jerrold R. Griggs, Ron Holzman, Daniel J. Kleitman

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let B be any family of 3-subsets of [n] = {1, ..., n} such that every i in [n] belongs to at most three members of B. It is shown here that there exists a 3 × n (0, 1)-matrix M such that every set of columns of M indexed by a member of B is linearly independent over GF(2). The proof depends on finding a suitable vertex-coloring for the associated 3-uniform hypergraph. This matrix result, which is a special case of a conjecture of Griggs and Walker, implies the corresponding special case of a conjecture of Chung, Frankl, Graham, and Shearer and of Faudree, Schelp, and Sós concerning intersecting families of subsets.

Original languageEnglish
Pages (from-to)306-315
Number of pages10
JournalJournal of Combinatorial Theory, Series A
Volume53
Issue number2
DOIs
Publication statusPublished - 1990

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Coloring
Intersecting Family
(0, 1)-matrices
Vertex Coloring
Subset
Uniform Hypergraph
Linearly
Imply
Family

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Representations of families of triples over GF(2). / Füredi, Z.; Griggs, Jerrold R.; Holzman, Ron; Kleitman, Daniel J.

In: Journal of Combinatorial Theory, Series A, Vol. 53, No. 2, 1990, p. 306-315.

Research output: Contribution to journalArticle

Füredi, Z. ; Griggs, Jerrold R. ; Holzman, Ron ; Kleitman, Daniel J. / Representations of families of triples over GF(2). In: Journal of Combinatorial Theory, Series A. 1990 ; Vol. 53, No. 2. pp. 306-315.
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