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Aug 15, 2012 at 4:48 comment added JSE Yes -- by "expander graph" I mean "infinite family of graphs with a spectral gap." Bad notation, I know.
Aug 15, 2012 at 4:06 comment added Igor Rivin It is pretty hard to construct a graph which is not expanding with some constant, and given a graph of a reasonable size, it is not so difficult to compute the expansion constant (the stupid algorithm is exponential, but for graphs up to around 30 vertices this should not be a problem). It is constructing an infinite family of such that is hard.
Aug 15, 2012 at 3:04 comment added Michael Lugo More generally, the probabilistic method (en.wikipedia.org/wiki/Probabilistic_method) as pioneered by Erdos comes to mind.
Aug 15, 2012 at 1:27 history answered JSE CC BY-SA 3.0