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

Charles Colbourn; Alan C H Ling; Gaetano Quattrocchi

doi:10.1016/j.disc.2007.09.038

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

Charles Colbourn, Alan C H Ling, Gaetano Quattrocchi

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A (K₄ - e)-design on v + w points embeds a Steiner triple system (STS) if there is a subset of v points on which the graphs of the design induce the blocks of a STS. It is established that w ≥ v / 3, and that when equality is met that such a minimum embedding of an STS (v) exists, except when v = 15.

Original language	English (US)
Pages (from-to)	5308-5311
Number of pages	4
Journal	Discrete Mathematics
Volume	308
Issue number	22
DOIs	https://doi.org/10.1016/j.disc.2007.09.038
State	Published - Nov 28 2008

Keywords

Design embedding
Graph design
Resolvable design
Steiner triple system

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.disc.2007.09.038

Cite this

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title = "Minimum embedding of Steiner triple systems into (K4 - e)-designs I",

abstract = "A (K4 - e)-design on v + w points embeds a Steiner triple system (STS) if there is a subset of v points on which the graphs of the design induce the blocks of a STS. It is established that w ≥ v / 3, and that when equality is met that such a minimum embedding of an STS (v) exists, except when v = 15.",

keywords = "Design embedding, Graph design, Resolvable design, Steiner triple system",

author = "Charles Colbourn and Ling, {Alan C H} and Gaetano Quattrocchi",

note = "Funding Information: Most of the work was carried out when the first two authors visited University of Catania. The hospitality of the department is greatly appreciated. The research of the first two authors is sponsored by an ARO grant DAAD19-01-1-0406. The research of the third author is sponsored by MIUR-Italy and CNR-GNSAGA. ",

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AU - Colbourn, Charles

AU - Ling, Alan C H

AU - Quattrocchi, Gaetano

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PY - 2008/11/28

Y1 - 2008/11/28

N2 - A (K4 - e)-design on v + w points embeds a Steiner triple system (STS) if there is a subset of v points on which the graphs of the design induce the blocks of a STS. It is established that w ≥ v / 3, and that when equality is met that such a minimum embedding of an STS (v) exists, except when v = 15.

AB - A (K4 - e)-design on v + w points embeds a Steiner triple system (STS) if there is a subset of v points on which the graphs of the design induce the blocks of a STS. It is established that w ≥ v / 3, and that when equality is met that such a minimum embedding of an STS (v) exists, except when v = 15.

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KW - Resolvable design

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