Almost all Steiner triple systems have perfect matchings

Kwan MA. 2020. Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. 121(6), 1468–1495.


Journal Article | Published | English

Scopus indexed
Abstract
We show that for any 𝑛 divisible by 3, almost all order- 𝑛 Steiner triple systems have a perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of perfect matchings in a Steiner triple system and show that almost all Steiner triple systems essentially attain this maximum. We accomplish this via a general theorem comparing a uniformly random Steiner triple system to the outcome of the triangle removal process, which we hope will be useful for other problems. Our methods can also be adapted to other types of designs; for example, we sketch a proof of the theorem that almost all Latin squares have transversals.
Publishing Year
Date Published
2020-12-01
Journal Title
Proceedings of the London Mathematical Society
Volume
121
Issue
6
Page
1468-1495
ISSN
eISSN
IST-REx-ID

Cite this

Kwan MA. Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. 2020;121(6):1468-1495. doi:10.1112/plms.12373
Kwan, M. A. (2020). Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.12373
Kwan, Matthew Alan. β€œAlmost All Steiner Triple Systems Have Perfect Matchings.” Proceedings of the London Mathematical Society. Wiley, 2020. https://doi.org/10.1112/plms.12373.
M. A. Kwan, β€œAlmost all Steiner triple systems have perfect matchings,” Proceedings of the London Mathematical Society, vol. 121, no. 6. Wiley, pp. 1468–1495, 2020.
Kwan MA. 2020. Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. 121(6), 1468–1495.
Kwan, Matthew Alan. β€œAlmost All Steiner Triple Systems Have Perfect Matchings.” Proceedings of the London Mathematical Society, vol. 121, no. 6, Wiley, 2020, pp. 1468–95, doi:10.1112/plms.12373.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 1611.02246

Search this title in

Google Scholar