Good point sequencings of Steiner triple systems

Erskine, Grahame and Griggs, Terry (2022). Good point sequencings of Steiner triple systems. Australasian Journal of Combinatorics, 84(3) pp. 431–439.

URL: https://ajc.maths.uq.edu.au/pdf/84/ajc_v84_p431.pd...

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 consecutive l points in the permutation contains a block. It is known that every STS(v) with v > 3 has a 3-good sequencing. Here 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.

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