# Math 38. Graph Theory

Spring 2008

Homework

The latest homework will always appear on top.

Homework 21. Due on Wednesday, May 28.

• Do Problems 7.2.6 and 7.2.8.

Homework 20. Due on Friday, May 23.

• Do Problem 7.2.3.

Homework 19. Due on Wednesday, May 21.

• Do Problems 6.1.13 and 6.1.30.

Homework 18. Due on Monday, May 19.

• Do Problem 5.2.21 (proof of uniqueness for the Turan graph).

Homework 17. Due on Friday, May 16.

• Do Problems 5.2.7 and 5.2.9.

Homework 16. Due on Wednesday, May 14.

• Do Problem 4.3.3 (network on handout) and determine the chromatic number of the graph on the handout.

Homework 15. Due on Friday, April 30.

• Study for in-class exam on Friday.

Homework 14. Due on Wednesday, April 30.

• Do Problem 3.1.28.

Homework 13. Due on Monday, April 28.

• Do Problem 3.1.8, and either 3.1.18 or 3.1.13.

Homework 12. Due on Friday, April 25.

• Prove that successively deleting the heaviest edge that isn't a cut edge yields a minimum-weight spanning tree.

Homework 11. Due on Wednesday, April 23.

• Do Problem 2.2.35 (Tarry's Algorithm).

Homework 10. Due on Monday, April 21.

• Prove that, given an Euler circuit in a digraph D, if the last exiting edge from every vertex except r is colored purple, then the purple edges constitute a spanning in-tree rooted at r. about the induction trap (1.3.26 and A.28).

• Do either Problem 1.2.43 or Problem 2.2.31.

Homework 9. Due on Friday, April 18.

• Read about the Matrix Tree Theorem (pp. 83-87) and about the induction trap (1.3.26 and A.28).

• Do Problems 2.2.2 and 2.2.7.

Homework 8. Due on Monday, April 14.

• Practice your Pruefer codes and study for hour exam!

Homework 7. Due on Friday, April 11.

• Read Section 2.1 from the book.

• Do Problems 2.1.18 and 2.1.20.

Homework 6. Due on Wednesday, April 9.

• Read Section 1.4 from the book.

• Do Problems 1.4.8 and 1.4.10.

Homework 5. Due on Monday, April 7.

• Read Section 1.3 from the book.

• Re-do (if necessary) Problems 1.2.26 and 1.2.29.

Homework 4. Due on Friday, April 4.

• Do Problems 1.2.26 and 1.2.29.

Homework 3. Due on Wednesday, April 2.

• Do Problems 1.2.3 and 1.2.15.

Homework 2. Due on Monday, March 31.

• Read Section 1.2 from the book.

• Find and draw all unlabeled graphs with 5 vertices.

Homework 1. Due on Friday, March 28.

• Read Section 1.1 from the book.

• Do Section 1.1, Problems 10 and 29.

There will be homework due on most class days. It will consist typically of a reading assignment (of the part of the book covered in class) and a problem or two. Collaboration is permitted, but you must name your collaborators and write up your work individually.