Construction of expanders and superconcentrators using Kolmogorov complexity

We show the existence of various versions of expander graphs using Kolmogorov complexity. This method seems superior to the usual probabilistic construction. It turns out that the best known bounds on the size of expanders and superconcentrators can be attained based on this method. In the case of (acyclic) superconcentrators we attain a density of about 34 edges/vertices. Furthermore, related graph properties are reviewed, like magnification, edge-magnification, and isolation, and we develop bounds based on the Kolmogorov approach. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 17: 64–77, 2000