Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tangles are Decided by Weighted Vertex Sets   We show that, given a $ k $-tangle $ \tau $ in a graph $ G $, there always
exists a weight function $ w\colon V(G)\to\mathbb{N} $ such that a separation $
(A,B) $ of $ G $ of order $ {<}k $ lies in $ \tau $ if and only if $ w(A)<w(B)
$, where $ w(U) := \sum_{u\in U}w(u) $ for $ U\subseteq V(G) $. We show that
the same result holds also for tangles of hypergraphs as well as for
edge-tangles of graphs, but not for edge-tangles of hypergraphs.

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The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat