High-girth Steiner triple systems

Pages 1059-1156 from Volume 200 (2024), Issue 3 by Matthew Kwan, Ashwin Sah, Mehtaab Sawhney, Michael Simkin

We prove a 1973 conjecture due to Erd\H os on the existence of Steiner triple systems with arbitrarily high girth.

Keywords

DOI

Milestones

Received: 14 January 2022
Revised: 23 January 2024
Accepted: 30 April 2024
Published online: 1 November 2024

Authors

Matthew Kwan

Institute of Science and Technology Austria (IST Austria), Klosterneuburg, Austria

Ashwin Sah

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

Mehtaab Sawhney

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

Current address:

Department of Mathematics, Columbia University, New York, NY, USA

Michael Simkin

Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA, USA

Current address:

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA