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Sun 4 Dec, 2005 10:53 pm
Let B be a set of boys, and suppose that each boy in B wishes to marry more than one of his girl friends. Find a necessary and sufficient condition for the harem problem to have a solution.
I was thinking perhaps we need to somehow replace each boy by several identical copies of himself, and then try to use Hall's theorem. But how?
I don't know Hall's theorem, but it seems you would want the size of G (the girls) to be greater than or equal to the size of B (the boys).