Re: [math-fun] planar graph of US states

Of course, this follows immediately from the fact that for any pre-edged graph with >= 5 vertices (and any symmetric probability model where all potential edges have a positive probability of existing), there's a positive chance q of there being a (literal) K_5. So for a graph with N times the number of vertices, the chance of a K_5 is 1 = (1-q)^N -> 0 as N -> oo. On 2013-02-18, at 3:14 PM, Warren Smith wrote:

[And the fraction of, e.g, N vertex planar graphs within N vertex graphs is asymptotically known... almost all graphs are nonplanar...]