تقرير
Saturation Numbers for Berge Cliques
| العنوان: | Saturation Numbers for Berge Cliques |
|---|---|
| المؤلفون: | English, Sean, Kritschgau, Jürgen, Nahvi, Mina, Sprangel, Elizabeth |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C35 |
| الوصف: | Let $F$ be a graph and $\mathcal{H}$ be a hypergraph, both embedded on the same vertex set. We say $\mathcal{H}$ is a Berge-$F$ if there exists a bijection $\phi:E(F)\to E(\mathcal{H})$ such that $e\subseteq \phi(e)$ for all $e\in E(F)$. We say $\mathcal{H}$ is Berge-$F$-saturated if $\mathcal{H}$ does not contain any Berge-$F$, but adding any missing edge to $\mathcal{H}$ creates a copy of a Berge-$F$. The saturation number $\mathrm{sat}_k(n,\text{Berge-}F)$ is the least number of edges in a Berge-$F$-saturated $k$-uniform hypergraph on $n$ vertices. We show \[ \mathrm{sat}_k(n,\text{Berge-}K_\ell)\sim \frac{\ell-2}{k-1}n, \] for all $k,\ell\geq 3$. Furthermore, we provide some sufficient conditions to imply that $\mathrm{sat}_k(n,\text{Berge-}F)=O(n)$ for general graphs $F$. Comment: 16 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2301.02973 |
| رقم الأكسشن: | edsarx.2301.02973 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |