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arXiv · 2504.19729

Faster Dynamic $(\Delta+1)$-Coloring Against Adaptive Adversaries

Maxime Flin·Magnús M. Halldórsson
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Abstract

We consider the problem of maintaining a proper $(\Delta + 1)$-vertex coloring in a graph on $n$-vertices and maximum degree $\Delta$ undergoing edge insertions and deletions. We give a randomized algorithm with amortized update time $\widetilde{O}( n^{2/3} )$ against adaptive adversaries, meaning that updates may depend on past decisions by the algorithm. This improves on the very recent $\widetilde{O}( n^{8/9} )$-update-time algorithm by Behnezhad, Rajaraman, and Wasim (SODA 2025) and matches a natural barrier for dynamic $(\Delta+1)$-coloring algorithms. The main improvements are in the densest regions of the graph, where we use structural hints from the study of distributed graph algorithms.

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Maxime Flin, Magnús M. Halldórsson. 2025-04-28. Faster Dynamic $(\Delta+1)$-Coloring Against Adaptive Adversaries. https://arxiv.org/abs/2504.19729

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