Fully Dynamic (? +1)-Coloring in <i>O</i> (1) Update Time

The problem of (? +1)-vertex coloring a graph maximum degree ? has been extremely well studied over the years in various settings and models. Surprisingly, for dynamic setting, almost nothing was known until recently. In SODA’18, Bhattacharya, Chakrabarty, Henzinger Nanongkai devised randomized algorithm maintaining +1)-coloring with O (log ?) expected amortized update time. this article, we present an improved that achieves (1) time show bound holds not only expectation but also high probability. Our starting point is state-of-the-art maximal matching (Solomon, FOCS’16). We carefully build on approach Solomon, but, due to inherent differences between problems, need deviate significantly from it several crucial highly nontrivial points. 1