Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $r$-coloring and maximum stable set problem in hypergraphs with
  bounded matching number and edge size   Motivated by the analogous questions in graphs, we study the complexity of
coloring and stable set problems in hypergraphs with forbidden substructures
and bounded edge size. Letting $\nu(G)$ denote the maximum size of a matching
in $H$, we obtain complete dichotomies for the complexity of the following
problems parametrized by fixed $r, k, s \in \mathbb{N}$: $r$-Coloring in
hypergraphs $G$ with edge size at most $k$ and $\nu(G) \leq s$; $r$-Precoloring
Extension in $k$-uniform hypergraphs $G$ with $\nu(G) \leq s$; $r$-Precoloring
Extension in hypergraphs $G$ with edge size at most $k$ and $\nu(G) \leq s$;
Maximum Stable Set in $k$-uniform hypergraphs $G$ with $\nu(G) \leq s$; Maximum
Weight Stable Set in $k$-uniform hypergraphs with $\nu(G) \leq s$; as well as
partial results for $r$-Coloring in $k$-uniform hypergraphs $\nu(G) \leq s$.
  We then turn our attention to $2$-Coloring in 3-uniform hypergraphs with
forbidden induced subhypergraphs, and give a polynomial-time algorithm when
restricting the input to hypergraphs excluding a fixed one-edge hypergraph.
Finally, we consider linear 3-uniform hypergraphs (in which every two edges
share at most one vertex), and show that excluding an induced matching in $G$
implies that $\nu(G)$ is bounded by a constant; and that $3$-coloring linear
$3$-uniform hypergraphs $G$ with $\nu(G) \leq 532$ is NP-hard.

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The categories of this paper are: nucl-th
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The categories of this paper are: econ
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph