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In a village there are an equal number of boys and girls of marriageable age. Each boy dates a certain number of girls and each girl dates a certain number of boys. Under what condition is it possible that every boy and girl gets married to one of their dates?(Polygamy and polyandry not allowed)

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What you actually have is a bipartite graph and you are looking for a perfect matching. The theorem that provides a characterization for such conditions is Hall's marriage theorem: There exists a perfect matching for the graph if and only if for any set of boys $B$, $|B|\leq|N(B)|$ where $N(B)$ denotes the set of girls that date at least one of the boys from $B$.

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ya you are right – kalpeshmpopat Mar 13 '13 at 9:08

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