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具有对数混合时间的图。本文提出一种具有常数混合时间的图的组合刻画。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，且强于具有近最优小集顶点扩展。