Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Treewidth of Line Graphs   The treewidth of a graph is an important invariant in structural and
algorithmic graph theory. This paper studies the treewidth of line graphs. We
show that determining the treewidth of the line graph of a graph $G$ is
equivalent to determining the minimum vertex congestion of an embedding of $G$
into a tree. Using this result, we prove sharp lower bounds in terms of both
the minimum degree and average degree of $G$. These results are precise enough
to exactly determine the treewidth of the line graph of a complete graph and
other interesting examples. We also improve the best known upper bound on the
treewidth of a line graph. Analogous results are proved for pathwidth.

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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: eess