MathCastle
Graph TheoryMediumBipartite Graphs and Matchings

Bipartite Graphs and Matchings · Medium problem

Men 1,2,31,2,3 rank women as 1:X,Y,Z1: X,Y,Z;   2:Y,Z,X\;2: Y,Z,X;   3:Z,X,Y\;3: Z,X,Y. Women rank men as X:2,3,1X: 2,3,1;   Y:3,1,2\;Y: 3,1,2;   Z:1,2,3\;Z: 1,2,3. Run the deferred-acceptance algorithm twice, once with the men proposing and once with the women proposing (men now only accepting or rejecting). For each run, add up the ranks (on his own list) that each man gets. What is the (women-proposing sum) MINUS (men-proposing sum)?