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* Princeton Discrete Math Seminar *
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Speaker: Nina Kamčev (University of Zagreb)
Thursday 23rd March, 3:00 in Fine Hall 224.
Title: The Turán density of tight cycles in three-uniform hypergraphs
Turán-type problems for hypergraphs have been an intriguing area of research.
Despite significant efforts, the Turán density of F is known for only a few
three-uniform hypergraphs F. This talk concerns Turán-type problems for
3-uniform tight cycles C_k, where the number of vertices k is not divisible by
3.
The Turán density of a hypergraph F is the maximum density of an n-vertex
hypergraph that does not contain any member of F. Mubayi and Rödl gave an
``iterated blow-up'' construction showing that the Turán density of C_5 is at
least 2sqrt{3}-3, and this bound is conjectured to be tight. Interestingly,
their construction also excludes C_k for larger k not divisible by 3, indicating
that it might be the extremal construction for these hypergraphs as well.
Indeed, we have recently shown that the Turán density of C_k is 2sqrt{3}-3 for
sufficiently large k, in a joint result with Shoham Letzter and Alexey
Pokrovskiy.
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