On the class of gamma-mixing graphs

Details On the class of gamma-mixing graphs On the class of gamma-mixing graphs

2012-03-30

arxiv.org/abs/1203.6880v1

Mathematics

Combinatorics

Scientific paper

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.

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