IEOR 6614, Spring 2007 : Homework 2

General Instructions

1. Please review the course information.
2. You must write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
3. Numbered problems are all from the textbook Network Flows .

Problems

1. Problem 13.14. Tree minimax result.
2. Problem 13.26. Updating a minimum spanning tree.
3. Problem 13.30. Most vital arcs.
4. Prove the following: Let G=(V,E) be a graph with non-negative edge weights w, and let T be the minimum spanning tree. You can assume the edge weights are unique. For any cycle C, let e_C be the maximum weight edge in the cycle. Let S = { e_C: C is a cycle in G } be the set of maximum weght edges in some cycle. Prove that S and T are disjoint sets.
5. Prove or disprove the following statement. Let G=(V,E) be a graph with non-negative edge weights w, and let T be the minimum spanning tree. Let H be a graph formed from G by adding 2 to each of the edge weights. T is a minimum spanning tree of H.

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• Homework 1
• Homework 3