  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.
