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To address the statement "men also have more sexual partners than women" using graph theory, we can model heterosexual relationships as a bipartite graph and analyze the implications. This approach helps us rigorously evaluate the statement, particularly in the context of averages, which is often implied in such claims.
The statement compares the number of sexual partners between men and women, typically interpreted as comparing the average number of partners. We will focus on heterosexual relationships for simplicity, as this is the most straightforward interpretation of the statement (though we can later consider extensions to other cases). In graph theory terms, we can represent heterosexual relationships as a bipartite graph:
- Let ( M ) be the set of all men, and ( W ) be the set of all women.
- An edge ( (m, w) ) exists between a man ( m \in M ) and a woman ( w \in W ) if they have