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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let the crown $C_{13}$ be the linear $3$-graph on $9$ vertices$\{a,b,c,d,e,f,g,h,i\}$ with edges $$E = \{\{a,b,c\}, \{a, d,e\}, \{b, f, g\},\{c, h,i\}\}.$$ Proving a conjecture of Gy\'arf\'as et. al., we show that forany crown-free linear $3$-graph $G$ on $n$ vertices, its number of edgessatisfy $$\lvert E(G) \rvert \leq \frac{3(n - s)}{2}$$ where $s$ is the numberof vertices in $G$ with degree at least $6$. This result, combined withprevious work, essentially completes the determination of linear Tur\'an numberfor linear $3$-graphs with at most $4$ edges.

Note on the Tur\'an number of the $3$-linear hypergraph $C_{13}$