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Plane Map <=> Planar Graph ?

  1. May 26, 2004 #1
    Plane Map <=> Planar Graph ??

    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.

  2. jcsd
  3. May 26, 2004 #2


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    I 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.
  4. May 26, 2004 #3
    yes basically, but why can there not be maps of non-planar graphs?
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