Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Facets and facet subgraphs of adjacency polytopes   Adjacency polytopes, a.k.a. symmetric edge polytopes, associated with
undirected graphs have been defined and studied in several
seemingly-independent areas including number theory, discrete geometry, and
dynamical systems. In particular, the authors are motivated by the study of the
algebraic Kuramoto equations of unmixed form whose Newton polytopes are the
adjacency polytopes.
  The interplay between the geometric structure of adjacency polytopes and the
topological structure of the underlying graphs is a recurring theme in recent
studies. In particular, "facet/face subgraphs" emerged as one of the central
concepts in describing this symmetry. Continuing along this line of inquiry we
provide a complete description of the correspondence between facets/faces of an
adjacency polytope and maximal bipartite subgraphs of the underlying connected
graph.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom