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The Triangle chromatic index of Steiner triple systems

Grannell, M.J.; Griggs, T.S and Hill, R. (2001). The Triangle chromatic index of Steiner triple systems. Australasian Journal of Combinatorics, 23 pp. 217–230.

URL: http://ajc.math.auckland.ac.nz/volume_contents.php...
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Abstract

In a Steiner triple system of order v, STS(v), a set of three lines intersecting pairwise in three distinct points is called a triangle. A set of lines containing no triangle is called triangle-free. The minimum number of triangle-free sets required to partition the lines of a Steiner triple system S, is called the triangle chromatic index of S. We prove that for all admissible v, there exists an STS (v) with triangle chromatic index at most 8√3v. In addition, by showing that the projective geometry PG(n,3) may be partitioned into O(6n/5) caps, we prove that the STS(v) formed the points and lines of the affine geometry AG(n,3) has triangle chromatic index at most Avs, where s=log6/(3log5)≈0.326186, and A is a constant. We also determine the values of the index for STS(v) with v≤13.

Item Type: Journal Article
ISSN: 1034-4942
Extra Information: Some of the symbols may not have transferred correctly into this bibliographic record.
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 2150
Depositing User: Mike Grannell
Date Deposited: 06 Jun 2006
Last Modified: 02 Dec 2010 19:46
URI: http://oro.open.ac.uk/id/eprint/2150
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