Graph theory problem | Mathematics | Page 1

winged kernel Sep 6, 2023, 2:17 PM

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Hey! I really have no idea how to solve this problem... I`ve tried to do some things involving contradiction, but did not get anything. Any ideas?
The problem: "Prove or disprove the following claim: for some n ≥ 3 (n boys
and n girls, for a total of 2n people), there exists a set of boys’ and girls’ preferences such
that every dating arrangement is stable."

green phoenixBOT Sep 6, 2023, 2:17 PM

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plucky yarrow Sep 6, 2023, 6:40 PM

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How do the preferences work?

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Because couldn’t you just be like “none of them want to date” and let that be a contradiction?

pastel ibex Sep 7, 2023, 2:42 AM

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I think preference is a total ranking for each person, so every boy wants to date every girl at least a little (and vice versa).

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What operation does "stable" use in this case?

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If it does exist, I'm guessing it's going to be a cyclic-looking arrangement.

#Graph theory problem