Planar graph

[bogdan]

What is the definition of a planar graph and which properties does it have ?

[lethe]

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.

[bogdan]

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...

[lethe]

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?

[bogdan]

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 )[6)]

[rutwig]

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.

[bogdan]

If only I could find those books...anyway...I fount something on the Internet...but it's so complicated...[:(]

[rutwig]

Originally posted by bogdan
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

http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/download.html