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Apr 3 2024

Combinatorics and Discrete Probability Seminar: Turán density of long tight cycle minus one hyperedge, by Jozsef Balogh

April 3, 2024

3:00 PM - 3:50 PM


1227 SEO


Chicago, IL

Jozsef Balogh (UIUC): Turán density of long tight cycle minus one hyperedge

Denote by C?? the 3-uniform hypergraph obtained by removing one hyperedge from the tight cycle on ? vertices. It is conjectured that the Turán density of C?5 is 1/4. In this paper, we make progress toward this conjecture by proving that the Turán density of C?? is 1/4, for every sufficiently large ? not divisible by 3. One of the main ingredients of our proof is a forbidden-subhypergraph characterization of the hypergraphs, for which there exists a tournament on the same vertex set such that every hyperedge is a cyclic triangle in this tournament.

A byproduct of our method is a human-checkable proof for the upper bound on the maximum number of almost similar triangles in a planar point set, which was recently proved using the method of flag algebras by Balogh, Clemen, and Lidický.

Joint work with Haoran Luo

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Marcus Michelen

Date posted

Apr 15, 2024

Date updated

Apr 15, 2024