Faithful enclosing of triple systems

A generalization of stern’s theorem

David C. Bigelow, Charles Colbourn

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

A triple system of order v and index λ is faithfully enclosed in a triple system of order w ≥ v and index µ ≥ λ when the triples induced on some v elements of the triple system of order w are precisely those from the triple system of order v. When λ = µ, faithful enclosing is embedding; when λ = 0, faithful enclosing asks for an independent set of size v in a triple system of order w. A generalization of Stern’s theorem for embedding is proved: A triple system of order v and index λ can be faithfully enclosed in a triple system of order w and index µ whenever w ≥ 2v + 1, µ ≥ λ and µ = 0 mod gcd(w - 2, 6).

Original languageEnglish (US)
Title of host publicationGraphs, Matrices, and Designs
PublisherCRC Press
Pages31-42
Number of pages12
ISBN (Electronic)0824787900, 9781351444385
ISBN (Print)9781138403987
DOIs
StatePublished - Jan 1 2017
Externally publishedYes

Fingerprint

Triple System
Faithful
Theorem
Independent Set
Generalization

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Faithful enclosing of triple systems : A generalization of stern’s theorem. / Bigelow, David C.; Colbourn, Charles.

Graphs, Matrices, and Designs. CRC Press, 2017. p. 31-42.

Research output: Chapter in Book/Report/Conference proceedingChapter

Bigelow, David C. ; Colbourn, Charles. / Faithful enclosing of triple systems : A generalization of stern’s theorem. Graphs, Matrices, and Designs. CRC Press, 2017. pp. 31-42
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