Dynamic 3-Coloring of Bipartite Graphs with Optimal Locality

Abstract

We give a dynamic graph algorithm which maintains a 3-coloring in bipartite graphs under edge insertions such that the coloring only changes within a radius of $O(\log n)$ around an inserted edge. In the context of locality theory in distributed graph algorithms, this gives an upper bound on the locality under the dynamic-LOCAL model. Our bound on the locality is tight, as the problem admits a matching $\Omega(\log n)$ lower bound in the stronger online-LOCAL model, by a result of Chang et al. [PODC 2024]. Thus, our result closes the gap between dynamic and online locality of this problem.