Good point sequencings of Steiner triple systems
Combinatorics
2022-04-07 v1
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.
Cite
@article{arxiv.2204.02732,
title = {Good point sequencings of Steiner triple systems},
author = {Grahame Erskine and Terry Griggs},
journal= {arXiv preprint arXiv:2204.02732},
year = {2022}
}
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9 pages