Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Nullstellensatz and DP-coloring of Graphs   We initiate the study of applying the Combinatorial Nullstellensatz to the
DP-coloring of graphs even though, as is well-known, the Alon-Tarsi theorem
does not apply to DP-coloring. We define the notion of good covers of prime
order which allows us to apply the Combinatorial Nullstellensatz to
DP-coloring. We apply these tools to DP-coloring of the cones of certain
bipartite graphs and uniquely 3-colorable graphs. We also extend a result of
Akbari, Mirrokni, and Sadjad (2006) on unique list colorability to the context
of DP-coloring. We establish a sufficient algebraic condition for a graph $G$
to satisfy $\chi_{DP}(G) \leq 3$, and we completely determine the DP-chromatic
number of squares of all cycles.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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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: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph