English

High-Girth Steiner Triple Systems

Combinatorics 2024-05-07 v4

Abstract

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

Cite

@article{arxiv.2201.04554,
  title  = {High-Girth Steiner Triple Systems},
  author = {Matthew Kwan and Ashwin Sah and Mehtaab Sawhney and Michael Simkin},
  journal= {arXiv preprint arXiv:2201.04554},
  year   = {2024}
}

Comments

Added details to some proofs. Final version, to appear in Annals of Mathematics

R2 v1 2026-06-24T08:47:54.240Z