How to create some large 3-regular planar graphs I'm looking for a way to produce very large (100-2000 vertices) 3-regular planar graphs.
I've tried to use plantri (plantri -m5 -v 100), but I was not able to produce only random examples (10-50 graphs) and the entire set of graphs with a lot of vertices is too big.
Any other place or way I can produce large graphs?
 A: A program like plantri is very fast considering that it can generate exactly one member of each isomorphism class - which is arguably the trickiest part.
If you only want a small number of random graphs, and you don't care too much about the uniformity of the random selection, then it seems like an approach like:


*

*Generate a random triangulation (T) with minimum degree 5 (-m5
flag,right?). It looks like the PlanarMap program of Gilles Schaeffer could do this. (see below).

*Form the dual of T to get your graph G. 

*Optionally check for duplicates - which is quite quick for planar
graphs.


Of course, now we have to do step 1) - but I find it hard to believe that there are no existing approaches for generating random triangulations...

Edit: So there is an approach to generating random planar triangulations due to Gilles Schaeffer (paper here) that claims to be :

This simple pseudo-algorithm is linear on average and gives in a few seconds random maps with up to one million edges or vertices

so it looks like it could handle your use case :)
