Mixing time bounds for edge flipping on regular graphs

Abstract

The edge flipping is a non-reversible Markov chain on a given connected graph, which is defined by Chung and Graham in [CG12]. In the same paper, its eigenvalues and stationary distributions for some classes of graphs are identified. We further study its spectral properties to show a lower bound for the rate of convergence in the case of regular graphs. Moreover, we show that a cutoff occurs at \frac{1}{4} n \log n for the edge flipping on the complete graph by a coupling argument.Comment: 16 pages. An error in the proof of Theorem 1.1 is corrected. The section on vertex flipping is removed. Presentation is revised. Note the change in the titl