Good point sequencings of Steiner triple systems

TL;DR

This paper investigates special point arrangements in Steiner triple systems that avoid blocks in consecutive points, proving existence for certain parameters and providing computational results for small systems.

Contribution

It establishes new existence results for l-good sequencings in Steiner triple systems, extending known cases and including computational findings.

Findings

Every STS(v) with v > 3 has a 3-good sequencing.

Every STS(v) with v >= 13 has a 4-good sequencing.

Every 3-chromatic STS(v) with v >= 15 has a 5-good sequencing.

Abstract

An l-good sequencing of a Steiner triple system of order v, STS(v), is a permutation of the points of the system such that no l consecutive points in the permutation contains a block. It is known that every STS(v) with v > 3 has a 3-good sequencing. It is proved that every STS(v) with v >= 13 has a 4-good sequencing and every 3-chromatic STS(v) with v >= 15 has a 5-good sequencing. Computational results for Steiner triple systems of small order are also given.