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

  • #1

Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
34,053
9,913
This looks trivial, and easy to prove yourself if you really want to. Assuming edges can cross each other, of course.
 
  • #3
FactChecker
Science Advisor
Gold Member
5,384
1,953
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.
 
  • #4
Stephen Tashi
Science Advisor
7,017
1,237
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.
 

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

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
7K
Replies
10
Views
763
Replies
8
Views
684
Replies
12
Views
2K
Replies
5
Views
588
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
10
Views
584
Top