Large girth approximate Steiner triple systems

@article{Bohman2018LargeGA,
  title={Large girth approximate Steiner triple systems},
  author={Tom Bohman and Lutz Warnke},
  journal={Journal of the London Mathematical Society},
  year={2018},
  volume={100}
}
  • T. BohmanL. Warnke
  • Published 3 August 2018
  • Mathematics
  • Journal of the London Mathematical Society
In 1973, Erdős asked whether there are n ‐vertex partial Steiner triple systems with arbitrary high girth and quadratically many triples. (Here girth is defined as the smallest integer g⩾4 for which some g ‐element vertex‐set contains at least g−2 triples.) 
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On a Conjecture of Erdős on Locally Sparse Steiner Triple Systems

This work proves the Erdős conjecture that one can find so-called ‘sparse’ Steiner triple systems with arbitrary parameters asymptotically by analysing a natural generalization of the triangle removal process.

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