Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Threshold for weak saturation stability   We study the weak $K_s$-saturation number of the Erd\H{o}s--R\'{e}nyi random
graph $\mathbbmsl{G}(n, p)$, denoted by $\mathrm{wsat}(\mathbbmsl{G}(n, p),
K_s)$, where $K_s$ is the complete graph on $s$ vertices. Kor\'{a}ndi and
Sudakov in 2017 proved that the weak $K_s$-saturation number of $K_n$ is
stable, in the sense that it remains the same after removing edges with
constant probability. In this paper, we prove that there exists a threshold for
this stability property and give upper and lower bounds on the threshold. This
generalizes the result of Kor\'{a}ndi and Sudakov. A general upper bound for
$\mathrm{wsat}(\mathbbmsl{G}(n, p), K_s)$ is also provided.

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The categories of this paper are: stat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org