Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform scrambles on graphs   A scramble on a connected multigraph is a collection of connected subgraphs
that generalizes the notion of a bramble. The maximum order of a scramble,
called the scramble number of a graph, was recently developed as a tool for
lower bounding divisorial gonality. We present results on the scramble of all
connected subgraphs with a fixed number of vertices, using these to calculate
scramble number and gonality both for large families of graphs, and for
specific examples like the $4$- and $5$-dimensional hypercube graphs. We also
study the computational complexity of the egg-cut number of a scramble.

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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys