# Thread: Points and line segments

1. ## Points and line segments

Draw 6 points on a plane. Can you connect each of them with 4 other points, in such a way that the line segments do not intersect?

2. ## Re: Points and line segments

Originally Posted by Alderamin
Draw 6 points on a plane. Can you connect each of them with 4 other points, in such a way that the line segments do not intersect?
You are looking for a planar graph of order six in which each vertex is of degree four.
Good luck. Tell us what you find.

3. ## Re: Points and line segments

I think I got it. Thanks for the help.

4. ## Re: Points and line segments

Originally Posted by Alderamin
I think I got it. Thanks for the help.
well damn...

nicely done. Did you come up with that yourself?

5. ## Re: Points and line segments

Originally Posted by Alderamin
I think I got it. Thanks for the help.
Yes, well done indeed. This exercise is getting you ready to be asked if $\bf{K}_6$ is planar?

6. ## Re: Points and line segments

Originally Posted by romsek
well damn...

nicely done. Did you come up with that yourself?
No, I followed Plato's hint.

7. ## Re: Points and line segments

Originally Posted by Plato
Yes, well done indeed. This exercise is getting you ready to be asked if $\bf{K}_6$ is planar?
Yes, if I understood well, it is planar, since "it can be drawn on the plane in such a way that its edges intersect only at their endpoints" (wiki).