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
(10:3012:30).
Problems for Math 408 and 708:
1. We showed in class that the vertexedge incidence matrices of all directed graphs and
bipartite undirected graphs are totally unimodular. However, in general, the vertexedge
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 (zeroone) 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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 Spring '10
 aa
 Operations Research, Graph Theory, Matrices, Optimization, consecutive ones property, vertexedge incidence matrices

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