On the class of graphs with strong mixing properties

Mikhail Isaev (1) , K.V Isaeva (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 MIPT - Moscow Institute of Physics and Technology [Moscow]

We study three mixing properties of a graph: large algebraic connectivity, large Cheeger constant (isoperimetric number) and large spectral gap from 1 for the second largest eigenvalue of the transition probability matrix of the random walk on the graph. We prove equivalence of this properties (in some sense). We give estimates for the probability for a random graph to satisfy these properties. In addition, we present asymptotic formulas for the numbers of Eulerian orientations and Eulerian circuits in an undirected simple graph.

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Mikhail Isaev, K.V Isaeva. On the class of graphs with strong mixing properties. Proceeding of MIPT, 2013, 5 (6), pp.44-54. ⟨hal-00684088v2⟩