Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ubiquity in graphs III: Ubiquity of locally finite graphs with extensive
  tree-decompositions   A graph $G$ is said to be ubiquitous, if every graph $\Gamma$ that contains
arbitrarily many disjoint $G$-minors automatically contains infinitely many
disjoint $G$-minors. The well-known Ubiquity conjecture of Andreae says that
every locally finite graph is ubiquitous.
  In this paper we show that locally finite graphs admitting a certain type of
tree-decomposition, which we call an extensive tree-decomposition, are
ubiquitous. In particular this includes all locally finite graphs of finite
tree-width, and also all locally finite graphs with finitely many ends, all of
which have finite degree. It remains an open question whether every locally
finite graph admits an extensive tree-decomposition.

33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs