Algorithms Homework 1 Solutions Instructor :

Figure 1: This is the example, illustrating the proof above. The black matching is M and the orange matching is M ′. The lists beside m,w shows their preference list. We know that m prefers his match in the black matching, w, to his match in the orange matching, w′. For purposes of contradiction, we assumed that w prefers m to m′. As you can see, this implies that the pair (m,w) is an instability, a contradiction.