# Almost all Steiner triple systems are almost resolvable

## TL;DR

This paper proves that for large enough order n divisible by 3, nearly all Steiner triple systems can be decomposed into almost all triples as disjoint perfect matchings, making them nearly resolvable.

## Contribution

It establishes that almost all Steiner triple systems are nearly resolvable, a significant advancement in understanding their structural properties.

## Key findings

- Almost all Steiner triple systems are almost resolvable.
- The result holds for all n divisible by 3.
- Most Steiner triple systems admit a near-decomposition into perfect matchings.

## Abstract

We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).