3-regular bipartite planar graphs appear in a variety of NP- / #P-complete problems. Suppose one wants to test the complexity of these problems via numerical experiments. Is there an efficient way to generate random planar cubic bipartite graphs?
I only know of algorithms that can efficiently generate random graphs with only subsets of the set of properties {cubic,planar,bipartite}, and it seems that generating those and then naively testing for the remainder of the properties would be terribly inefficient if one wants graphs with >100 vertices.