Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized saturation problems for cliques, paths, and stars   A graph $G$ is $F$-saturated if it does not contain any copy of $F$, but the
addition of any missing edge in $G$ creates at least one copy of $F$. Inspired
by work of Alon and Shikhelman regarding a similar question for $F$-free
graphs, Kritschgau, Methuku, Tait, and Timmons introduced the parameter of
$\text{sat}_H(n,F)$ to denote the minimum number of copies of some subgraph $H$
in an $F$-saturated graph on $n$ vertices. In this paper, we address this
generalized saturation problem with special focus on $\text{sat}_{K_r}(n,S_t)$
and $\text{sat}_{S_r}(n,S_t)$ This relates to recent work by Chakraborti and
Loh regarding $\text{sat}_{K_r}(n,K_t)$ and by Ergemlidze, Methuku, Tait, and
Timmons regarding $\text{sat}_{S_r}(n,K_t)$. We also provide some results
regarding paths and arbitrary trees.

14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph