Seminar in Discrete Mathematics - Bernard Lidický

The seminars in Discrete Mathematics  are aimed at researchers, employees, and students.

This week's seminar is given by Bernard Lidický, Iowa State.

Title: The Hypergraph Turán Densities of Tight Cycles Minus an Edge 

Abstract: A tight $\ell$-cycle minus an edge $C_\ell^-$ is the $3$-graph on the vertex set $[\ell]$, where any three consecutive vertices in the string $123\ldots\ell 1$ form an edge. We show that for every $\ell\ge 5$, $\ell$ not divisible by $3$, the extremal number is:

\[ex\left(C_\ell^-,n\right)=\tfrac1{24}n^3+O(n\ln n)=\left(\tfrac14+o(1)\right){n\choose 3}. \]

 We determine the extremal graph up to $O(n)$ edge edits. The proof is based on flag algebra calculations. This is a joint work with Connor Mattes and Florian Pfender