quick planar question
I have to draw a network (edges without arrow-heads) for the following ordered pairs in such a way that the edges DO NOT cross each other:
(1,2) (1,3) (1,4) (2,3) (2,4) (2,5) (2,6) (3,4) (3,5) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7).
Basically this means, I need to write 1,2,3,4,5,6,7 on a sheet of paper and draw lines from the first digit in the ordered pair to the second digit in the ordered pair. This is for a logic class.
Is this even possible? I've tried a few different configurations and it doesn't seem like it's going to work. Also, is there a way just to look at the pairs and know instantly it's impossible? Like I know, (1,4) (1,5) (1,6) (2,4) (2,5) (2,6) (3,4) (3,5) (3,6) is impossible.
It took a while but it is a planar graph.
Thanks a lot. I really appreciate it. I could have sworn it wouldn't exist.