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DOI: 10.4230/LIPIcs.ITCS.2026.92

A Combinatorial Characterization of Constant Mixing Time

Authors: Lap Chi Lau and Raymond Liu

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

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.

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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)

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@InProceedings{lau_et_al:LIPIcs.ITCS.2026.92,
  author =	{Lau, Lap Chi and Liu, Raymond},
  title =	{{A Combinatorial Characterization of Constant Mixing Time}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{92:1--92:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.92},
  URN =		{urn:nbn:de:0030-drops-253792},
  doi =		{10.4230/LIPIcs.ITCS.2026.92},
  annote =	{Keywords: Random walks, mixing time, bipartite density, spectral graph theory}
}

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A Combinatorial Characterization of Constant Mixing Time

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