Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, October 03, 2019, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Stefan Glock

High-girth Steiner triple systems and a Turán problem of Brown, Erdős and Sós

A Steiner triple system of order n is a set of triples in an n-set such that every pair is covered by exactly one triple. Kirkman characterised in 1847 for which n these exist. Erdős conjectured in 1973 that for fixed g and any sufficiently large admissible order n, there exists a Steiner triple system of order n with girth at least g, meaning that there are no j points which span at least j-2 triples for any 3 < j < g. We prove this conjecture asymptotically by analysing a random process. In this talk, we will discuss this result and also briefly discuss connections to a Turán problem of Brown, Erdős and Sós. partly joined with Daniela Kühn, Allan Lo and Deryk Osthus


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