Mathematics 243 (Combinatorial and Discrete Geometry)

Review: Examination II (Part II)

prepared by:

Joseph Malkevitch
Mathematics Department
York College (CUNY)
Jamaica, NY 11451

email: joeyc@cunyvm.cuny.edu
web page: http://www.york.cuny.edu/~malk

1. Use Konig's alternating path algorithm to find a larger matching for the graph below, starting with the partial matching indicated using bold edges:

2. Use Konig's algorithm to find a maximum cardinality matching for the graphs below:

3. Using the matrix of jobs (rows) and workers (columns) below find:

a. A matching whose total weight is as large as possible

b. A matching whose total weight is as small as possible

c. A matching whose maximum weight edge is as small as possible

d. A matching whose smallest weight edge is as large as possible.

e. What interpretation of the numbers above might lead one to want to minimize the total weight of a matching?

f. What interpretation of the numbers above might lead one to want to maximize the the total weight of a matching?