I'm attempting to prove the following proposition:
For n>2 lines arranged in the plane, in general position, it is possible to color the vertices of the lines with 3 colors such that no 2 adjacent vertices have the same color.
I've been trying to prove via induction, but can't seem to get beyond the following thoughts:
- Obviously we start with a base case of n=3 and (trivially) prove it can be colored.
- We could, when given n lines, subtract one and accept that for n-1 it is true. But I'm unable to find how to prove that n is true from n-1 being true.
Would graph theory be helpful here?