6 . 042 J / 18 . 062 J , Fall ’ 05 : Mathematics for Computer Science October 3 Prof . Albert

A 1994 University of Chicago study entitled The Social Organization of Sexuality found that on average men have 74% more opposite­gender partners than women, confirming a view that men are more promiscuous. But whoever reported this finding was lying or confused! We’ll show you how to use the properties of vertex degrees in a graph to prove this. Let’s recast opposite­gender partnering in graph theoretic terms. Let G be a graph where the set of vertices V consists of everyone in America. Now each vertex either represents either a male or a female, so we can partition V into two subsets: M , which contains all the male vertices, and F , which contains all the female vertices. Let’s draw all the M vertices on the left and the F vertices on the right: