Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: List Coloring and $n$-monophilic graphs   In 1990, Kostochka and Sidorenko proposed studying the smallest number of
list-colorings of a graph $G$ among all assignments of lists of a given size
$n$ to its vertices. We say a graph $G$ is $n$-monophilic if this number is
minimized when identical $n$-color lists are assigned to all vertices of $G$.
Kostochka and Sidorenko observed that all chordal graphs are $n$-monophilic for
all $n$. Donner (1992) showed that every graph is $n$-monophilic for all
sufficiently large $n$. We prove that all cycles are $n$-monophilic for all
$n$; we give a complete characterization of 2-monophilic graphs (which turns
out to be similar to the characterization of 2-choosable graphs given by Erdos,
Rubin, and Taylor in 1980); and for every $n$ we construct a graph that is
$n$-choosable but not $n$-monophilic.

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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph