We show that the number of labeled cubic planar graphs on n vertices with n even is asymptotically αn-7/2ρ-nn!, where ρ-1 ... 3.13259 and α are analytic constants. We show also that the chromatic number of a random cubic planar graph that is chosen uniformly at random among all the labeled cubic planar graphs on n vertices is three with probability tending to e-ρ4/4! ... 0.999568 and four with probability tending to 1 - e-ρ4/4! as n → ∞ with n even. The proof given combines generating function techniques with probabilistic arguments. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007
['Manuel Bodirsky', 'Mihyun Kang', 'Mike Löffler', 'Colin McDiarmid']
Random cubic planar graphs