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Improved Bounds for Coloring Locally Sparse Hypergraphs

Author Fotis Iliopoulos

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ACM Subject Classification
  • Theory of computation → Generating random combinatorial structures
  • Theory of computation → Pseudorandomness and derandomization
  • Theory of computation → Random search heuristics
  • Theory of computation → Random network models
Keywords
  • hypergaph coloring
  • semi-random method
  • locally sparse
  • random hypergraphs

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Abstract

We show that, for every k ≥ 2, every k-uniform hypergaph of degree Δ and girth at least 5 is efficiently (1+o(1))(k-1) (Δ / ln Δ)^{1/(k-1)}-list colorable. As an application we obtain the currently best deterministic algorithm for list-coloring random hypergraphs of bounded average degree.

Cite As Get BibTex

Fotis Iliopoulos. Improved Bounds for Coloring Locally Sparse Hypergraphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 39:1-39:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.39

Author Details

Fotis Iliopoulos
  • Institute for Advanced Study, Princeton, NJ, USA
  • Princeton University, NJ, USA

Funding

This material is based upon work directly supported by the IAS Fund for Math and indirectly supported by the National Science Foundation Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the Simons Collaboration on Algorithms and Geometry

Acknowledgements

The author is grateful to Dimitris Achlioptas, Irit Dinur and anonymous reviewers for detailed comments and feedback.

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