Fully Dynamic (Δ+1)-Coloring in Constant Update Time

by   Sayan Bhattacharya, et al.

The problem of (vertex) (Δ+1)-coloring a graph of maximum degree Δ 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 (Δ+1)-coloring with O(logΔ) expected amortized update time. In this paper, we present a (Δ+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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