MathCastle
Graph TheorySuperchallengeBipartite Graphs and Matchings

Bipartite Graphs and Matchings · Superchallenge problem

Men A,B,C,D,EA,B,C,D,E rank women V,W,X,Y,ZV,W,X,Y,Z as A ⁣: ⁣V,W,Z,Y,XA\!:\!V,W,Z,Y,X; B ⁣: ⁣Y,V,W,X,ZB\!:\!Y,V,W,X,Z; C ⁣: ⁣Z,W,V,X,YC\!:\!Z,W,V,X,Y; D ⁣: ⁣W,X,V,Y,ZD\!:\!W,X,V,Y,Z; E ⁣: ⁣X,Z,Y,V,WE\!:\!X,Z,Y,V,W. Women rank men as V ⁣: ⁣D,B,E,C,AV\!:\!D,B,E,C,A; W ⁣: ⁣C,A,D,E,BW\!:\!C,A,D,E,B; X ⁣: ⁣E,D,A,B,CX\!:\!E,D,A,B,C; Y ⁣: ⁣D,E,C,B,AY\!:\!D,E,C,B,A; Z ⁣: ⁣B,E,D,A,CZ\!:\!B,E,D,A,C. Among all stable matchings for this profile, what is the SMALLEST possible combined total (sum of all five men's ranks plus all five women's ranks)?