Minimum embedding of Steiner triple systems into (K4 - e)-designs II

Alan C H Ling, Charles Colbourn, Gaetano Quattrocchi

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A (K4 - e)-design of order v + w embeds a given Steiner triple system if there is a subset of v points on which the graphs of the design induce the blocks of the original Steiner triple system. It has been established that w ≥ v / 3, and that when equality is met, such a minimum embedding of an STS(v) exists, except when v = 15. Equality only holds when v ≡ 15, 27 (mod 30). One natural question is: What is the smallest order w such that some STS(v) can be embedded into a (K4 - e)-design of order v + w? We solve the problem for 7 of the 10 congruence classes modulo 30.

Original languageEnglish (US)
Pages (from-to)400-411
Number of pages12
JournalDiscrete Mathematics
Volume309
Issue number2
DOIs
StatePublished - Jan 28 2009

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Steiner Triple System
Equality
Congruence
Modulo
Subset
Graph in graph theory
Design

Keywords

  • Embedding

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Minimum embedding of Steiner triple systems into (K4 - e)-designs II. / Ling, Alan C H; Colbourn, Charles; Quattrocchi, Gaetano.

In: Discrete Mathematics, Vol. 309, No. 2, 28.01.2009, p. 400-411.

Research output: Contribution to journalArticle

Ling, Alan C H ; Colbourn, Charles ; Quattrocchi, Gaetano. / Minimum embedding of Steiner triple systems into (K4 - e)-designs II. In: Discrete Mathematics. 2009 ; Vol. 309, No. 2. pp. 400-411.
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