The University College London (UCL) Combinatorics Seminar is held every Monday at 4–5pm during term time.

The venue for this week’s seminar is Room 706 at 25, Gordon Street.

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Next Speaker

• 2nd December 2024 - Jared León (University of Warwick)

  The Turán density of the tight 5-cycle minus one edge

  
  

  This is joint work with Bodnar, Liu and Pikhurko. Results similar to ours were independently obtained by Lidický, Mattes and Pfender.

  The tight $\ell$-cycle minus one edge $C_\ell^{3-}$ is the $3$-graph on ${1,\dots,\ell}$ consisting of $\ell-1$ consecutive triples in cyclic order. We show that, for every $\ell\geqslant 5$ not divisible by $3$, the Turán density of $C_{\ell}^{3-}$ is $1/4$, and also show a stability and a finer structure result. This proves a conjecture of Mubayi, Sudakov and Pikhurko from 2011 and extends the results of Balogh and Luo, who established analogous claims for all sufficiently large $\ell$. In this talk, I will present the idea behind the main proof.