Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2605.11049 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
Sommario:
- Motivated by the Erdős--Sós bipartite link conjecture, Füredi (Oberwolfach, 2004) asked for the asymptotic maximum edge density $π_{\mathrm{link}}(t)$ of $3$-graphs in which the link graph of every vertex is $t$-partite. Goldwasser's recursive blow-up construction based on projective planes gives the lower bound $π_{\mathrm{link}}(t)\ge 1-t^{-1}-(2+o_t(1))t^{-2}$ whenever $t-1$ is a prime power. In this note, we prove the upper bound $π_{\mathrm{link}}(t)\le 1-t^{-1}-t^{-2}/12$ for every $t \ge 2$. Together with Goldwasser's construction, this determines, up to a constant factor, the correct order of the gap between $π_{\mathrm{link}}(t)$ and the trivial averaging upper bound $1-t^{-1}$ for all prime-power values of $t-1$. In fact, our argument applies in the more general setting of $3$-graphs with no generalized daisies, equivalently, $3$-graphs in which the link graph of every vertex is $K_{t+1}$-free. We also establish an analogous upper bound for the positive $(r-1)$-codegree Turán density of generalized daisies.