Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak saturation stability   We study wsat$(G,H)$, the minimum number of edges in a weakly $H$-saturated
subgraph of $G$. We prove that wsat$(K_n,H)$ is stable (remains the same after
independent removal of every edge of $K_n$ with a constant probability) for all
pattern graphs $H$ such that there exists a `local' set of edges that
percolates in $K_n$ (this is true, for example, for $K_s$, $K_{s,s}$ and
$K_{s,s+1}$). Also, we find a threshold probability for the weak
$K_{1,t}$-saturation stability.

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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: eess