A randomized dynamic algorithm maintains a proper (Δ+1)-coloring against adaptive adversaries in Õ(n^{2/3}) amortized update time, improving the prior Õ(n^{8/9}) bound.
Halld´ orsson, Fabian Kuhn, and Alexandre Nolin
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Faster Dynamic $(\Delta+1)$-Coloring Against Adaptive Adversaries
A randomized dynamic algorithm maintains a proper (Δ+1)-coloring against adaptive adversaries in Õ(n^{2/3}) amortized update time, improving the prior Õ(n^{8/9}) bound.