How many edges must a planar graph with $n$ nodes have that it is sure that it is
In particular, are all planar graphs with $n$ nodes and $3n-6$ edges ($n\ge 4$) triconnected ?
I tried to use Euler's formula, but it only holds for connected planar graphs. And in the case, that the graph is connected, but not biconnected, the faces need not be bounded by a cycle. How can I deal with this case ?
Since a planar graph with $n$ nodes and $3n-9$ edges ($n\ge 4$) need not be connected (see comment below), at least $3n-8$ edges are required.