Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Not all simplicial polytopes are weakly vertex-decomposable   In 1980 Provan and Billera defined the notion of weak $k$-decomposability for
pure simplicial complexes. They showed the diameter of a weakly
$k$-decomposable simplicial complex $\Delta$ is bounded above by a polynomial
function of the number of $k$-faces in $\Delta$ and its dimension. For weakly
0-decomposable complexes, this bound is linear in the number of vertices and
the dimension. In this paper we exhibit the first examples of non-weakly
0-decomposable simplicial polytopes.

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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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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: quant-ph
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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: adap-org
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The categories of this paper are: eess
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The categories of this paper are: hep-lat