Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Jun 13, 2016 #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?
     
  2. jcsd
  3. Jun 13, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    This looks trivial, and easy to prove yourself if you really want to. Assuming edges can cross each other, of course.
     
  4. Jun 13, 2016 #3

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    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.
     
  5. Jun 14, 2016 #4

    Stephen Tashi

    User Avatar
    Science Advisor

    Look at material about "planar graphs". Not all graphs are planar graphs.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted