Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on simultaneous representation problem for interval and
  circular-arc graphs   In this short note, we show two NP-completeness results regarding the
\emph{simultaneous representation problem}, introduced by Lubiw and Jampani.
The simultaneous representation problem for a given class of intersection
graphs asks if some $k$ graphs can be represented so that every vertex is
represented by the same interval in each representation. We prove that it is
NP-complete to decide this for the class of interval and circular-arc graphs in
the case when $k$ is a part of the input and graphs are not in a sunflower
position.

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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: gr-qc