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Improved Bounds for Randomly Colouring Simple Hypergraphs

Authors Weiming Feng , Heng Guo , Jiaheng Wang

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Author Details

Weiming Feng
  • School of Informatics, University of Edinburgh, UK
Heng Guo
  • School of Informatics, University of Edinburgh, UK
Jiaheng Wang
  • School of Informatics, University of Edinburgh, UK

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 947778).

Cite AsGet BibTex

Weiming Feng, Heng Guo, and Jiaheng Wang. Improved Bounds for Randomly Colouring Simple Hypergraphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.25

Abstract

We study the problem of sampling almost uniform proper q-colourings in k-uniform simple hypergraphs with maximum degree Δ. For any δ > 0, if k ≥ 20(1+δ)/δ and q ≥ 100Δ^({2+δ}/{k-4/δ-4}), the running time of our algorithm is Õ(poly(Δ k)⋅ n^1.01), where n is the number of vertices. Our result requires fewer colours than previous results for general hypergraphs (Jain, Pham, and Vuong, 2021; He, Sun, and Wu, 2021), and does not require Ω(log n) colours unlike the work of Frieze and Anastos (2017).

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
Keywords
  • Approximate counting
  • Markov chain
  • Mixing time
  • Hypergraph colouring

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