## Math 38

### Graph Theory

Homework

Homework will be assigned for most class periods and will be due the following class period. Both homework assignments and solutions will be posted to the webpage. Please take the time to write up your solutions neatly and carefully! Late homework will not be accepted but your lowest three homework scores will be dropped.

You must cite other books or online sources if you use them to help solve a problem. If you enjoy working in groups, I encourage you to work with others in the class to solve the homework problems, but all homework is to be written up independently.

Number Due Date Problems Solutions
1 Friday, 4/3 Section 1.1: #12, 13, 30 Solutions
2 Monday, 4/6 Section 1.1: #10
Section 1.2: #18, 30
Solutions
3 Wednesday, 4/8 Section 1.2: #10, 24, 29 Solutions
4 Friday, 4/10 Section 1.2: #40
Section 1.3: #14, 32
Solutions
- Monday, 4/12 No Assignment
5 Wednesday, 4/15 Section 1.4: #8, 9
Section 2.1: #27
Solutions
6 Friday, 4/17 Section 2.1: #6, 18, 20 Solutions
7 Monday, 4/20 Section 2.2: #1, 7, 8 Solutions
- Wednesday, 4/22 No Assignment
8 Friday, 4/24 Section 2.3: #10
Also: Consider the algorithm where you successively delete the heaviest edge that is not a cut edge. Either prover that this always results in a minimum-weight spanning tree or give a counterexample.
Solutions
- Monday, 4/27 No Assignment (Exam Today) Exam Solutions
9 Wednesday, 4/29 Section 2.3: #20
Section 3.1: #8
Solutions
- Friday, 5/1 No Assignment
10 Monday, 5/4 Section 1.1: #14
Section 3.1: #9, 18
Solutions
11 Wednesday, 5/6 Section 3.1: #24
And also: Extra Problem
Solutions
- Friday, 5/8 No Assignment
12 Monday, 5/11 Section 4.1: #9, 10
Section 4.2: #4
Solutions
13 Wednesday, 5/13 Section 4.2: #1
Section 4.3: #2, 10
Solutions (Graphs)
- Friday, 5/15 No Assignment
14 Monday, 5/18 Section 5.1: #11, 15, 33 Solutions
- Wednesday, 5/20 No Assignment (Take-Home Due Friday)
- Friday, 5/22 Take-Home Exam Exam Solutions
- Monday, 5/25 No Class (Memorial Day)
- Wednesday, 5/27 No Assignment
15 Friday, 5/29 Section 6.1: #13, 14, 30
The girth of a graph is the length of the shortest cycle.
Solutions (Graphs)
16 Monday, 6/1 Section 8.3: #3a, 3b, 18a
In class, I used the notation R(3,3,...,3) for what the book is calling R_k(3;2)
Solutions