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

[paizhaulski]

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?

 

[mfb]

This looks trivial, and easy to prove yourself if you really want to. Assuming edges can cross each other, of course.

 

[FactChecker]

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.

 

[Stephen Tashi]

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.