Any graph is "drawable" on a 2D surface?

  • #1
Are there any theorems that say something formal about the fact that any graph is drawable on a 2D surface, and can be mapped to a 2D array of pixels if the pixels are infinitely small?
 

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  • #2
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This looks trivial, and easy to prove yourself if you really want to. Assuming edges can cross each other, of course.
 
  • #3
FactChecker
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When you say that, it implies that there is some way to distinguish between edges that cross at a point which is not a vertex and edges that meet at a vertex. In general, there will be lines crossing with no vertex there.
 
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  • #4
Stephen Tashi
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Are there any theorems that say something formal about the fact that any graph is drawable on a 2D surface, and can be mapped to a 2D array of pixels if the pixels are infinitely small?

Look at material about "planar graphs". Not all graphs are planar graphs.
 

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