Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Pairwise Compatibility of Some Graph (Super)Classes   A graph G=(V,E) is a pairwise compatibility graph (PCG) if there exists an
edge-weighted tree T and two non-negative real numbers `d' and `D' such that
each leaf `u' of T is a node of V and the edge `(u,v) belongs to E' iff `d <=
d_T(u, v) <= D' where d_T(u, v) is the sum of weights of the edges on the
unique path from `u' to `v' in T. The main issue on these graphs consists in
characterizing them.
  In this note we prove the inclusion in the PCG class of threshold tolerance
graphs and the non-inclusion of a number of intersection graphs, such as disk
and grid intersection graphs, circular arc and tolerance graphs. The
non-inclusion of some superclasses (trapezoid, permutation and rectangle
intersection graphs) follows.

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The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc