Which degree sequences are planar-graphical, that means for which degree sequences $$d_1,...,d_n$$ $$d_1\le...\le d_n$$ exists a PLANAR graph that has this degree sequence ?
I found some links in the internet, but I did not find a concrete classification. I know Euler's polyeder formula and that at least one vertex must have degree less than $6$ and some similar restrictions, but I would like to have some more powerful conditions.
There is no complete classification of the degree sequences of planar graphs as of today. However, I do have an example for you of an infinite number of similar degree sequences that always contain a planar graph:
$ (N,N,N,N,4,4,4,4,...) $, where $ N > 4 $ and the number of $ 4's $ in the sequence is equal to $ (N-2)^2 $.