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Beyond Brooks: (Δ-1)-Coloring in Semi-Streaming

Authors Maxime Flin , Magnús M. Halldórsson

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Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Graph coloring
  • streaming algorithm

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Abstract

Reed [J. Comb. Theory B, 1999] showed that graphs of maximum degree Δ ⩾ 10^14 without Δ-cliques are (Δ-1)-colorable. We design a one-pass semi-streaming algorithm for computing such a coloring. Additionally, we prove that any one-pass (Δ-k)-coloring algorithm for 0 ⩽ k < (Δ+1)/2 requires Ω(n(k+1)) space.

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Maxime Flin and Magnús M. Halldórsson. Beyond Brooks: (Δ-1)-Coloring in Semi-Streaming. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 92:1-92:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.92

Author Details

Maxime Flin
  • Aalto University, Espoo, Finland
Magnús M. Halldórsson
  • Reykjavik University, Iceland

Funding

  • Flin, Maxime: Supported in part by the Research Council of Finland, Grants 359104 and 363558. Part of this work was done while M. Flin was working at Reykjavik University, funded by the Icelandic Research Fund, Grant 2310015-053.
  • Halldórsson, Magnús M.: Supported by the Icelandic Research Fund, Grant 2511609.

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