Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on Shannon Capacity and Ramsey Numbers from Product of Graphs   In this note we study Shannon capacity of channels in the context of
classical Ramsey numbers. We overview some of the results on capacity of noisy
channels modelled by graphs, and how some constructions may contribute to our
knowledge of this capacity.
  We present an improvement to the constructions by Abbott and Song and thus
establish new lower bounds for a special type of multicolor Ramsey numbers. We
prove that our construction implies that the supremum of the Shannon capacity
over all graphs with independence number 2 cannot be achieved by any finite
graph power. This can be generalized to graphs with any bounded independence
number.

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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph