High-Girth Steiner Triple Systems
Matthew Kwan, Ashwin Sah, Mehtaab Sawhney, Michael Simkin
TL;DR
This paper proves a long-standing conjecture by Erdős from 1973, demonstrating the existence of Steiner triple systems with arbitrarily high girth, advancing combinatorial design theory.
Contribution
It establishes the existence of high-girth Steiner triple systems, resolving a decades-old open problem in combinatorics.
Findings
Confirmed the existence of Steiner triple systems with arbitrarily high girth
Resolved Erdős's 1973 conjecture
Contributed to combinatorial design theory
Abstract
We prove a 1973 conjecture due to Erd\H{o}s on the existence of Steiner triple systems with arbitrarily high girth.
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Taxonomy
Topicsgraph theory and CDMA systems · Limits and Structures in Graph Theory · Finite Group Theory Research