Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial cubes with pre-hull number at most 1   We prove that a connected bipartite graph G is a partial cube if and only if
the set of attaching points of any copoint of G is convex. A consequence of
this result is that any connected bipartite graph with pre-hull number at most
1 is a partial cube. We show that the class of partial cubes with pre-hull
number at most 1 is closed under gated subgraphs, gated amalgams and cartesian
products.

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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin