Parallel Batch Dynamic Vertex Coloring in $O(\log Δ)$ Amortized Update Time

We present the first parallel batch-dynamic algorithm for maintaining a proper $(Δ+ 1)$-vertex coloring. Our approach builds on a new sequential dynamic algorithm inspired by the work of Bhattacharya et al. (SODA'18). The resulting randomized algorithm achieves $O(\log Δ)$ expected amortized update time and, for any batch of $b$ updates, has parallel span $O(\operatorname{polylog} b + \operatorname{polylog} n)$ with high probability.