Constant-time dynamic (∆+1)-coloring

Abstract

We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (∆ + 1)-vertex coloring of a graph with maximum degree at most ∆. This improves upon the previous O(log ∆)-time algorithm by Bhattacharya et al. (SODA 2018). We show that our result does not only have optimal running time, but is also optimal in the sense that already deciding whether a ∆-coloring exists in a dynamically changing graph with maximum degree at most ∆ takes Ω(log n) time per operation