Constant-Time Dynamic (Δ+1)-Coloring

Authors Monika Henzinger , Pan Peng

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Monika Henzinger
  • University of Vienna, Faculty of Computer Science, Vienna, Austria
Pan Peng
  • Department of Computer Science, University of Sheffield, Sheffield, UK

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Monika Henzinger and Pan Peng. Constant-Time Dynamic (Δ+1)-Coloring. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 53:1-53:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (Δ+1)-vertex coloring of a graph with maximum degree at most Δ. This improves upon the previous O(log Δ)-time algorithm by Bhattacharya et al. (SODA 2018). Our algorithm uses an approach based on assigning random ranks to vertices and does not need to maintain a hierarchical graph decomposition. We show that our result does not only have optimal running time, but is also optimal in the sense that already deciding whether a Δ-coloring exists in a dynamically changing graph with maximum degree at most Δ takes Ω(log n) time per operation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Dynamic graph algorithms
  • Graph coloring
  • Random sampling


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