Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Max Weight Independent Set in graphs with no long claws: An analog of
  the Gy\'arf\'as' path argument   We revisit recent developments for the Maximum Weight Independent Set problem
in graphs excluding a subdivided claw $S_{t,t,t}$ as an induced subgraph
[Chudnovsky, Pilipczuk, Pilipczuk, Thomass\'{e}, SODA 2020] and provide a
subexponential-time algorithm with improved running time
$2^{\mathcal{O}(\sqrt{n}\log n)}$ and a quasipolynomial-time approximation
scheme with improved running time $2^{\mathcal{O}(\varepsilon^{-1} \log^{5}
n)}$.
  The Gy\'arf\'as' path argument, a powerful tool that is the main building
block for many algorithms in $P_t$-free graphs, ensures that given an
$n$-vertex $P_t$-free graph, in polynomial time we can find a set $P$ of at
most $t-1$ vertices, such that every connected component of $G-N[P]$ has at
most $n/2$ vertices. Our main technical contribution is an analog of this
result for $S_{t,t,t}$-free graphs: given an $n$-vertex $S_{t,t,t}$-free graph,
in polynomial time we can find a set $P$ of $\mathcal{O}(t \log n)$ vertices
and an extended strip decomposition (an appropriate analog of the decomposition
into connected components) of $G-N[P]$ such that every particle (an appropriate
analog of a connected component to recurse on) of the said extended strip
decomposition has at most $n/2$ vertices.

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The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat