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.

翻译：经典谱图理论刻画了对数混合时间的图结构。本文提出常数混合时间图的组合刻画方法。该组合刻画基于小集二分密度条件，该条件弱于具有近最优谱半径的条件，但强于具有近最优小集顶点扩展的条件。