Which degree sequences $d_1,…,d_n$ are planar-graphical?

• 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.

$(N,N,N,N,4,4,4,4,...)$, where $N > 4$ and the number of $4's$ in the sequence is equal to $(N-2)^2$.
• This seems like a very trivial result in this direction. Maybe a bit more interesting is that an $r$-regular planar graph on $n$ vertices always exists provided (1) $rn$ is even, the necessary condition for regular graphs (2) $\frac{rn}{2} \le 3n-6$, Euler's condition for planar graphs, and (3) $(r,n)$ is not $(4,7)$ or $(5,14)$. (source, I think) – Misha Lavrov Jul 18 '18 at 21:58