How Many for a Given Number of Points?

How big of a graph do you need something like a very good triangle would be? What if you had four points all connected to each other so it makes like a little square with an x through it Yeah, how many do you need to guarantee that you get that and I think you need 18 17 or 18 I think 17 You can take 17 points. You can draw all the possible 17 times 16 divided by two connections between them And together those ones plus all the different multiples that you can get should generate the whole group. But once you get to 18 you're guaranteed to have one Hmm So this is some very hard combinatorics problem as soon as we get up to five and six