---Bipartite Matching--- define bipartite graph.
Timetabling and Matching example (1):
Let x1, x2, and x3 represent 3 teachers teaching 4 classes ,
,
,
and
for these time periods:
A teaching schedule with the smallest possible number of periods can be set up as follows:
So in general the above teaching schedule can be represented by a bipartite graph G. A teaching schedule for one period corresponds to a ``matching'' in G.
Timetabling and Matching example (2): Suppose we have n classes and m teachers. Let the sign X to indicate which class to be taught by which teacher(s) (one lesson of one hour a day).
Next, construct a bipartite graph G. Fixing the time periods, the problem becomes a matching problem. See Figure 14.
Figure 14: Teachers-classes bipartite graph.