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One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming

Author Avinandan Das

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LIPIcs.SWAT.2026.15.pdf
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ACM Subject Classification
  • Theory of computation → Streaming models
Keywords
  • Graph Coloring
  • Semi-streaming algorithms
  • Lower bounds

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Abstract

This paper investigates the semi-streaming complexity of k-partial coloring, a generalization of proper graph coloring. For k ≥ 1, a k-partial coloring requires that each vertex v in an n-node graph is assigned a color such that at least min{k, deg(v)} of its neighbors are assigned colors different from its own. This framework naturally extends classical coloring problems: specifically, k-partial (k+1)-coloring and k-partial k-coloring generalize (Δ+1)-proper coloring and Δ-proper coloring, respectively.
Prior works of Assadi, Chen, and Khanna [SODA 2019] and Assadi, Kumar, and Mittal [TheoretiCS 2023] show that both (Δ+1)-proper coloring and Δ-proper coloring admit one-pass randomized semi-streaming algorithms. We explore whether these efficiency gains extend to their partial coloring generalizations and reveal a sharp computational threshold: while k-partial (k+1)-coloring admits a one-pass randomized semi-streaming algorithm, the k-partial k-coloring remains semi-streaming intractable, effectively demonstrating a "dichotomy of one color" in the streaming model.

Cite As Get BibTex

Avinandan Das. One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.15

Author Details

Avinandan Das
  • Aalto University, Finland

Funding

This work was supported in part by the Research Council of Finland, Grants 363558 and 359104.

Acknowledgements

Avinandan would like to thank Pierre Fraigniaud and Adi Rosén for proposing the problem of k-partial (k+1)-coloring and many discussions.

References

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