Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bound for the $(d-2)$-leaky forcing number of $Q_d$ and
  $\ell$-leaky forcing number of $GP(n,1)$   Leaky-forcing is a recently introduced variant of zero-forcing that has been
studied for families of graphs including paths, cycles, wheels, grids, and
trees. In this paper, we extend previous results on the leaky forcing number of
the d-dimensional hypercube, $Q_d$, to show that the $(d-2)$-leaky forcing
number of $Q_d$ is at most $2^{d-1}$. We also examine a question about the
relationship between the size of a minimum $\ell$-leaky-forcing set and a
minimum zero-forcing set for a graph $G$.

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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: econ