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Stochastics and Statistics Seminar Series

Large girth approximate Steiner triple systems

December 14, 2018 @ 11:00 am - 12:00 pm

Lutz Warnke (Georgia Institute of Technology)


Abstract: In 1973 Erdos 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 \ge 4 for which some g-element vertex-set contains at least g-2 triples.)

We answer this question, by showing existence of approximate Steiner triple systems with arbitrary high girth. More concretely, for any fixed \ell \ge 4 we show that a natural constrained random process typically produces a partial Steiner triple system with (1/6-o(1))n^2 triples and girth larger than \ell. The process iteratively adds random triples subject to the constraint that the girth remains larger than \ell. Our result is best possible up to the o(1)-term, which is a negative power of n.

Joint work with Tom Bohman.


December 14, 2018
11:00 am - 12:00 pm
Event Category:




Speaker Name(s)
Lutz Warnke
Speaker Affiliation
Georgia Institute of Technology

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