Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fully Dynamic $(\Delta+1)$-Coloring in Constant Update Time   The problem of (vertex) $(\Delta+1)$-coloring a graph of maximum degree
$\Delta$ has been extremely well-studied over the years in various settings and
models. Surprisingly, for the dynamic setting, almost nothing was known until
recently. In SODA'18, Bhattacharya, Chakrabarty, Henzinger and Nanongkai
devised a randomized data structure for maintaining a $(\Delta+1)$-coloring
with $O(\log \Delta)$ expected amortized update time. In this paper, we present
a $(\Delta+1)$-coloring data structure that achieves a constant amortized
update time and show that this time bound holds not only in expectation but
also with high probability.

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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci