Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Parameterized Complexity Of Grid Contraction   For a family of graphs $\mathcal{G}$, the $\mathcal{G}$-\textsc{Contraction}
problem takes as an input a graph $G$ and an integer $k$, and the goal is to
decide if there exists $F \subseteq E(G)$ of size at most $k$ such that $G/F$
belongs to $\mathcal{G}$. Here, $G/F$ is the graph obtained from $G$ by
contracting all the edges in $F$. In this article, we initiate the study of
\textsc{Grid Contraction} from the parameterized complexity point of view. We
present a fixed parameter tractable algorithm, running in time $c^k \cdot
|V(G)|^{\mathcal{O}(1)}$, for this problem. We complement this result by
proving that unless \ETH\ fails, there is no algorithm for \textsc{Grid
Contraction} with running time $c^{o(k)} \cdot |V(G)|^{\mathcal{O}(1)}$. We
also present a polynomial kernel for this problem.

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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an