Structure of Romantic and Sexual relationship

[Redbelly98]

... why are there no trapezoids?

... does it not strike anyone else as a bit odd that this whole thing turned out to be planar?

Indeed. Where are the concave polygons, dodecahedra, and 4-dimensional hypercubes? Clearly the data has been doctored with.

 

[KingNothing]

Indeed. Where are the concave polygons, dodecahedra, and 4-dimensional hypercubes? Clearly the data has been doctored with.

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.

 

[jobyts]

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? :tongue2:

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?

 

[Office_Shredder]

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?

 

[DaveC426913]

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.

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[CRGreathouse]

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
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F-+-F
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  M

No, K_4 is planar:

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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.

 

[DaveC426913]

No, K_4 is planar:

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  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.)

 

[CRGreathouse]

Minor (ha, ha) correction: planar graphs can't contain K_5 or K_3,3 or any subdivision of either. (Obvious only in my own head.)

I can see that there are some groups that cannot be made, even allowing for circuitous paths.

Well you can make them, just not on a plane without crossing.K_3,3 could be three males and three females, where each person is adjacent to/has had a romantic relationship with everyone of the opposite sex.