What is the definition of a planar graph and which properties does it have ?
a planar graph is one which can be drawn in a plane with no self-intersections. i believe the simplest nonplanar graph is the inscribed pentagram.
Well...I know that...
But isn't there an "abstract" definition which explains what a planar graph is without using the concept of "plan" ?
Only relations between the components of the graph...
there are some theorems about when a graph is planar or not. but you want to do what now? define a planar graph without using a plane?
Aaa...those theorems sound interesting...that's what I need...
Where can I find them ?
(I want to define a plane using a planar graph )
See the book of F. Harary. He gives a complete review starting from the famous theorem of Kuratowski. The booklet by O. Ore does also deal a bit with planarity of graphs.
If only I could find those books...anyway...I fount something on the Internet...but it's so complicated...
The books cited are not available on the net, since they were written in 1967 and 1968. However, have a look at
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