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Balanced Steiner Triple Systems

✍ Scribed by Charles Colbourn; Lucien Haddad; Václav Linek

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 302 KB
Volume: 78
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2767

No coin nor oath required. For personal study only.

✦ Synopsis

and v 15, a 3-chromatic Steiner triple system of order v all of whose 3-colorings are equitable.

1997 Academic Press

1. Introduction

A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that every pair of X is contained in exactly one triple of B. It is well known that a necessary and sufficient condition for a STS(v) to exist is that v#1 or 3 (mod 6). An r-coloring of a STS(v) is a map , : X Ä [1, ..., r] such that at least two vertices of every triple receive different colors, i.e., such that no triple is monochromatic. Equivalently, an r-coloring is a partition of the vertex set X into r parts, called color classes, none of which contains a triple of B. If a STS can be r-colored but not (r&1)-colored, then the system is r-chromatic. A coloring of a STS is equitable if the cardinalities of the color classes differ by at most one. The notions of r-coloring, chromatic article no. TA972767 292 0097-3165Â97 25.00

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