Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crossing-critical graphs with large maximum degree   A conjecture of Richter and Salazar about graphs that are critical for a
fixed crossing number $k$ is that they have bounded bandwidth. A weaker
well-known conjecture of Richter is that their maximum degree is bounded in
terms of $k$. In this note we disprove these conjectures for every $k\ge 171$,
by providing examples of $k$-crossing-critical graphs with arbitrarily large
maximum degree.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an