Question

Trying to make a love dodecahedron problem

Information below

Answer 1

If you ever heard the of the term love triangle, this is a lot more (or at least, I'm trying to make it more) complex. The above is a dodecahedron, with each vertices representing a person in the system. Each edge represents an interaction between each person. For example, since vertices A and B are connected, A might want them to be a couple, but B might only be interested in S.

There are 20 people in all, and 30 total interactions. However, 40% of the people are men, and there are some bisexual/homosexual relationships for both genders. A face is satisfied if the 5 people making up the vertices of the face only have one relationship. However, there are some vertices which are strictly homosexual or straight.

How can I turn this into a problem? What would the solution to that problem be? I'm guessing I have to set certain vertices certain preferences, such as J is strictly homosexual.

One easy problem (I guess) would be how many faces could be satisfied if each vertices had only one connection, as I said before above.