Let $G$ be a graph. We say an $r$-uniform hypergraph $H$ is a Berge-$G$ if there exists a bijection $\phi: E(G)\to E(H)$ such that $e\subseteq\phi(e)$ for each $e\in E(G)$. Given a family of $r$-uniform hypergraphs $\mathcal{F}$ and an $r$-uniform hypergraph $H$, a spanning sub-hypergraph $H'$ of $H$ is $\mathcal{F}$-saturated in $H$ if $H'$ is $\mathcal{F}$-free, but adding any edge in $E(H)\backslash E(H')$ to $H'$ creates a copy of some $F\in\mathcal{F}$. The saturation number of $\mathcal{F}$ is the minimum number of edges in an $\mathcal{F}$-saturated spanning sub-hypergraph of $H$. In this paper, we asymptotically determine the saturation number of Berge stars in random $r$-uniform hypergraphs.
@article{10_37236_9302,
author = {Lele Liu and Changxiang He and Liying Kang},
title = {Saturation number of {Berge} stars in random hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {4},
doi = {10.37236/9302},
zbl = {1454.05080},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9302/}
}
TY - JOUR
AU - Lele Liu
AU - Changxiang He
AU - Liying Kang
TI - Saturation number of Berge stars in random hypergraphs
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/9302/
DO - 10.37236/9302
ID - 10_37236_9302
ER -
%0 Journal Article
%A Lele Liu
%A Changxiang He
%A Liying Kang
%T Saturation number of Berge stars in random hypergraphs
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/9302/
%R 10.37236/9302
%F 10_37236_9302
Lele Liu; Changxiang He; Liying Kang. Saturation number of Berge stars in random hypergraphs. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9302
