Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharper Lower Bounds in the Maximum Degree and Diameter Bounded Subgraph
  Problem in the Mesh   The Maximum Degree and Diameter Bounded Subgraph Problem (MaxDDBS) asks:
given a host graph G, a bound on maximum degree \Delta, and a diameter D, what
is the largest subgraph of the host graph with degree bounded by \Delta and
diameter bounded by D? In this paper, we investigate this problem when the host
graph is the k-dimensional mesh. We provide lower bounds for the size of the
largest subgraph of the mesh satisfying MaxDDBS for all k and \Delta > 3 that
agree with the known upper bounds up to the first two terms, and show that for
\Delta = 3, the lower bounds are at least the same order of growth as the upper
bounds.

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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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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: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin