Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free choosability of the cycle   A graph $G$ is free $(a,b)$-choosable if for any vertex $v$ with $b$ colors
assigned and for any list of colors of size $a$ associated with each vertex
$u\ne v$, the coloring can be completed by choosing for $u$ a subset of $b$
colors such that adjacent vertices are colored with disjoint color sets. In
this note, a necessary and sufficient condition for a cycle to be free
$(a,b)$-choosable is given. As a corollary, some choosability results are
derived for graphs in which cycles are connected by a tree structure.

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The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
30
The categories of this paper are: q-alg