New in Mathematica 9 › Enhanced Graphs and Networks

Assignment Problems

A math department would like to offer seven courses. There are eight professors, each of whom is willing to teach certain courses. Find a maximal matching where professors only teach courses they are interested in teaching.

Build a bipartite graph between professors and courses they are interested in teaching.

In[1]:=

g = \!\(\*
GraphicsBox[
NamespaceBox["NetworkGraphics",
DynamicModuleBox[{Typeset`graph = HoldComplete[
Graph[{"Anne", "Kathy", "Erica", "Josh", "Rose", "Tim", "Vince", 
          "Emmy", "M501", "M347", "M448", "M425", "M507", "M515", 
          "M444"}, {{{2, 9}, {5, 9}, {2, 10}, {5, 10}, {8, 10}, {4, 
          11}, {6, 11}, {7, 11}, {1, 12}, {2, 12}, {7, 12}, {4, 13}, {
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          Null}, {GraphLayout -> "BipartiteEmbedding", VertexLabels -> {
Placed["Name", Center]}, VertexLabelStyle -> {
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The maximum flow from all professors to all courses show the matching.

In[2]:=

In[3]:=

Out[3]=