Plane Map <=> Planar Graph ??

[Jummeh]

Hi,
Wondering if anyone can help me to find some kind of proof that all Plane Maps can be represented by planar graphs and vice versa... for all Planar Graphs exists a Plane Map?

I did a quick search without much luck.

Thanks

[AKG]

Hi,
Wondering if anyone can help me to find some kind of proof that all Plane Maps can be represented by planar graphs and vice versa... for all Planar Graphs exists a Plane Map?

I did a quick search without much luck.

ThanksI can only gave a rough guess, I may not even give an answer relevant to the question, but if I understand you, then each "region" or "country" on the map can be represented by a vertex of the graph, and every "border" between "regions" on the map can be represented by an edge on the graph.

[Jummeh]

yes basically, but why can there not be maps of non-planar graphs?