Structure of Romantic and Sexual relationship

P: 216
 Quote by KingNothing Funny man, but I'm actually serious about the graph being 100% planar. It does seem strange to me, although I can't quite figure out what it means for sex.
Were you hoping for a 3D pornographic picture of students having sex?

A 2D graph is enough to explain this relationship. We understand the 6 month time dimension is not shown here. Is that what you are talking about?
 Emeritus Sci Advisor PF Gold P: 4,500 I think the question is it's curious that you can draw all those figures and avoid having to cross lines. For example, how would yo do this with a group of five people, all of who have had sex with each other?
 P: 15,319 I see KingNothing's point. There could theoretically be groups of relationships that cannot be represented without crossing lines (or without requiring a third dimension to the graph). Following OfficeShredders lead, I was about to ask what the simplest group of relationships is. OfficeShredder went for the group of five, but he missed the simpler one: 4 people. i.e. a tetrahedron. 4 people, all of whom have had romantic relationships with each other, cannot be represented in only 2 dimensions without crossing lines. And that sheds light on the answer to KingNothing's point. This simplest relationship requires some statistically highly unlikely connections. 4 people all having had relationships with each other is unlikely enough, but to do so, it requires a minimum of two same-sex relationships.  M /|\ F-+-F \|/ M
HW Helper
P: 3,684
 Quote by DaveC426913 Following OfficeShredders lead, I was about to ask what the simplest group of relationships is. OfficeShredder went for the group of five, but he missed the simpler one: 4 people. i.e. a tetrahedron. 4 people, all of whom have had romantic relationships with each other, cannot be represented in only 2 dimensions without crossing lines. And that sheds light on the answer to KingNothing's point. This simplest relationship requires some statistically highly unlikely connections. 4 people all having had relationships with each other is unlikely enough, but to do so, it requires a minimum of two same-sex relationships.  M /|\ F-+-F \|/ M
No, K_4 is planar:

  M
/ \\
F---F|
\ //
M
Kuratowski's theorem says that a graph is planar iff it avoids K_5 (OfficeShredder's example) and K_3,3. I can't conveniently ASCII art K_3,3 for you, but it's much easier to imagine in this context since doesn't require homosexual relationships.
P: 15,319
 Quote by CRGreathouse No, K_4 is planar:  M / \\ F---F| \ // M Kuratowski's theorem says that a graph is planar iff it avoids K_5 (OfficeShredder's example) and K_3,3. I can't conveniently ASCII art K_3,3 for you, but it's much easier to imagine in this context since doesn't require homosexual relationships.
Oh, right. I had a hidden assumption of using only straight lines.

I don't know Kuratowskian math, but reading up on it, I can see that there are some groups that cannot be made, even allowing for circuitous paths. This seems highly reminescent of the 5 house puzzle. (Shoot, I can't remember what it's called. It the one where you have to join 5 people to 5 houses without any paths crossing.)