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"Chris Smith" <cdsmith_at_twu.net> wrote in message news:MPG.1f07b8374b49cf619896f9_at_news.altopia.net...
> 2. Identify all of the regions. Regions are the empty spaces on your
> paper, and are separated by edges from the graph. The blank space
> outside of where you've drawn the graph DOES count as a region, so there
> is always at least one. If the graph is a tree, for example, then there
> is only one region, so the dual only has one vertex.
Doesn't region identification depend on the topology of the space? If your graph were on the surface of a torus, wouldn't you come up with possibly different regions? (viz. the seven color map theorem for the surface of a torus) Received on Sun Jun 25 2006 - 07:32:16 CDT