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Graph TheoryHardBipartite Graphs and Matchings

Bipartite Graphs and Matchings · Hard problem

Men 1,2,3,41,2,3,4 rank women as 1:P,Q,R,S1: P,Q,R,S;   2:P,R,S,Q\;2: P,R,S,Q;   3:P,S,Q,R\;3: P,S,Q,R;   4:Q,P,S,R\;4: Q,P,S,R. Women rank men as P:3,1,4,2P: 3,1,4,2;   Q:1,4,2,3\;Q: 1,4,2,3;   R:2,4,1,3\;R: 2,4,1,3;   S:4,1,2,3\;S: 4,1,2,3. Running the men-proposing deferred-acceptance algorithm to completion, how many proposals are made IN TOTAL (counting every proposal, including those later rejected)?