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A Combinatorial Characterization of Constant Mixing Time

Authors Lap Chi Lau, Raymond Liu

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LIPIcs.ITCS.2026.92.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
Keywords
  • Random walks
  • mixing time
  • bipartite density
  • spectral graph theory

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Abstract

Classical spectral graph theory characterizes graphs with logarithmic mixing time. In this work, we present a combinatorial characterization of graphs with constant mixing time. The combinatorial characterization is based on the small-set bipartite density condition, which is weaker than having near-optimal spectral radius and is stronger than having near-optimal small-set vertex expansion.

Cite As Get BibTex

Lap Chi Lau and Raymond Liu. A Combinatorial Characterization of Constant Mixing Time. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 92:1-92:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.92

Author Details

Lap Chi Lau
  • University of Waterloo, Canada
Raymond Liu
  • University of Waterloo, Canada

Funding

  • Lau, Lap Chi: Supported by an NSERC Discovery Grant.
  • Liu, Raymond: Supported by an NSERC Discovery Grant.

Acknowledgements

We thank Thatchaphol Saranurak for discussions on length-constrained expanders that inspired the study in this work.

References

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