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Homework 10: Graphs part 1 Solution

Problems

    1. (15 pts) Exercise 22.1-5.

    2. (15 pts) Exercise 22.2-6.

    3. (15 pts) Exercise 22.2-7.

    4. (10 pts) Exercise 22.3-7.

    5. (10 pts) Exercise 22.3-10.

    6. (15 pts) Exercise 22.3-12.

    7. (20 pts) Exercise 22.4-5.

    8. (15 pts) Two special vertices s and t in the undirected graph G=(V,E) have the fol-lowing property: any path from s to t has at least 1 + jV j=2 edges. Show that all paths from s to t must have a common vertex v (not equal to either s or t) and give an algorithm with running time O(V+E) to nd such a node v.

    9. (Extra credit 25) Problem 22-3.

    10. (Extra credit 25) Problem 22-4.

    11. (25 pts) Exercise 23.1-3.

    12. (25 pts) Exercise 23.2-2.

    13. (25 pts) Exercise 23.2-4.

    14. (25 pts) Exercise 23.2-5.

    15. (Extra credit 40 pts) Problem 23-1.

    16. (Extra credit 30 pts) Exercise 23.1-11.

    17. (Extra credit 30 pts) Write the code for Kruskal algorithm in a language of your choice. You will rst have to read on the disjoint sets datastructures and operations (Chapter 21 in the book) for an e cient implementation of Kruskal trees.









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