English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Denote by $\mathcal{C}^-_{\ell}$ the $3$-uniform hypergraph obtained byremoving one hyperedge from the tight cycle on $\ell$ vertices. It isconjectured that the Tur\'an density of $\mathcal{C}^-_{5}$ is $1/4$. In thispaper, we make progress toward this conjecture by proving that the Tur\'andensity of $\mathcal{C}^-_{\ell}$ is $1/4$, for every sufficiently large $\ell$not divisible by $3$. One of the main ingredients of our proof is aforbidden-subhypergraph characterization of the hypergraphs, for which thereexists a tournament on the same vertex set such that every hyperedge is acyclic triangle in this tournament.  A byproduct of our method is a human-checkable proof for the upper bound onthe maximum number of almost similar triangles in a planar point set, whichrecently was proved using flag algebra by Balogh, Clemen, and Lidick\'y.

Tur\'an density of long tight cycle minus one hyperedge