Flat graph

I have a Planar graph with n

nodes and e

edges that cut the plain into a section s

.

What is the upper limit for s

as a function of n

and e

and e/n

?

I am trying to find how little memory I can count on using any code.

It is easy to show that it is e

not more than n*(n-1)/2

, but I feel that it will be a small integer. For the case n ~= 10

, I have a fixed node position that overestimates the limit by 2x.