Abstract
We present an algorithm which inn 3 (logn)3 time constructs a 3-regular expander graph onn vertices. In each step we substitute a pair of edges of the graph by a new pair of edges so that the total number of cycles of lengths=⌊clogn⌋ decreases (for some fixed absolute constantc). When we reach a local minimum in the number of cycles of lengths the graph is an expander.
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