Second Homework Assignment for Math 408 and 708 Due: Friday, October 8th, 2010, in class. Note: The midterm will take place in class on Friday, October 22nd (10:30-12:30). Problems for Math 408 and 708: 1. We showed in class that the vertex-edge incidence matrices of all directed graphs and bipartite undirected graphs are totally unimodular. However, in general, the vertex-edge incidence matrices of undirected graphs are not totally unimodular. Give an example where this happens. 2. Chapter 2 problem 2. 3. Chapter 2 problem 3. 4. Chapter 3 problem 1. 5. Chapter 3 problem 2. Additional problems for Math 708: 6. Chapter 2 problem 4. 7. A binary (zero-one) matrix has the consecutive ones property if its columns can be rearranged so that the ones in each of its rows are consecutive. Show that any matrix with the consecutive ones property is totally unimodular. Remark: This is the transpose of question 3.3 in the text, however note that you can do it without using the generalized necessary condition. 8. Chapter 3 problem 4.
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