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arXiv · 2511.21868

A Combinatorial Characterization of Constant Mixing Time

Lap Chi Lau·Raymond Liu
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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.

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Lap Chi Lau, Raymond Liu. 2025-11-26. A Combinatorial Characterization of Constant Mixing Time. https://arxiv.org/abs/2511.21868

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