The course grade will be calculated as follows, out of 660 points total:
You can check your grades via Moodle.
Your grade total will be converted to a letter grade according to the following scale:
A+ | ≥ 620 | B+ | ≥ 490 | C+ | ≥ 360 | D+ | ≥ 250 |
A | ≥ 570 | B | ≥ 440 | C | ≥ 320 | D | ≥ 210 |
A- | ≥ 530 | B- | ≥ 400 | C- | ≥ 280 | D- | ≥ 180 |
It is possible to take the course for 4 credits rather than 3, at the cost of extra homework questions and more difficult exams. If you want to do this, you need to register at the math office in Altgeld Hall soon after the start of the course.
There will be 10 homework assignments, to be turned in at the beginning of class the day they are due. Of these homework assignments, the top 8 homework scores will determine your grade. Each assignment is graded out of 20 points, for a total of 160. The only extra credit given will be a 1-point bonus for typesetting your homework (for example, but not necessarily, in LaTeX); graph diagrams can still be hand-drawn.
If you cannot attend class, you can submit a scanned copy or a photo of your homework by e-mail before class begins. Please do not do this if you can attend class.
If the homework assignment is received after class on the due date, but before the next class, it will be accepted as late, for a 2-point penalty. Homework will not be accepted after the next class for any reason.
There will be three evening midterm exams: Wednesday 2/14 and Wednesday 3/14 from 7pm to 8:30pm in Talbot 103, and Wednesday 4/18 from 7pm to 8:30pm in Engineering Hall Room 106B8. Correspondingly, three lectures will be canceled, not necessarily in the same week as the midterm exams; these are also marked in the syllabus below.
The final exam will be given on Monday, May 7, 1:30-4:30pm, in 245 Altgeld Hall (our usual classroom).
The course follows chapters 1-7 of the textbook Introduction to Graph Theory by D. B. West. The syllabus below will initially describe a tentative plan for what parts of the textbook will be covered when. As the semester progresses, I will update the syllabus with information about what actually happened in class, adjustments to my plans for the future, and links to homework assignments.
Date | Chapter | Details | Homework |
Wed January 17 | Chapter 1 Fundamentals |
Section 1.1: What is a graph? | |
Fri January 19 | Section 1.1: Isomorphic graphs | ||
Mon January 22 | Section 1.2: Paths, cycles, and trails | ||
Wed January 24 | Section 1.2: Eulerian circuits | ||
Fri January 26 | Section 1.3: Vertex degrees | HW 1 due | |
Mon January 29 | Section 1.3: Graphic sequences | ||
Wed January 31 | Section 1.4: Directed graphs | ||
Fri February 2 | Section 1.4: Tournaments | HW 2 due | |
Mon February 5 | Chapter 2 Trees |
Section 2.1: Trees and forests | |
Wed February 7 | Section 2.1: More on distance | ||
Fri February 9 | Section 2.2: Spanning trees | HW 3 due | |
Mon February 12 | Section 2.2: Counting trees | ||
Wed February 14 | Section 2.3: Optimization | Exam: 7pm in Talbot 103 (Topics) | |
Fri February 16 | No class | ||
Mon February 19 | Chapter 3 Matchings |
Section 3.1: Matchings; Berge's theorem | |
Wed February 21 | Section 3.1: Hall's theorem | ||
Fri February 23 | Section 3.1: Vertex and edge covers | HW 4 due | |
Mon February 26 | Section 3.2: Stable matchings | ||
Wed February 28 | Section 3.3: Tutte's theorem | ||
Fri March 2 | Section 3.3: The Berge–Tutte formula | HW 5 due | |
Mon March 5 | Section 3.3: Petersen's theorem | ||
Wed March 7 | Chapter 4 Connectivity |
Section 4.1: Initial definitions | |
Fri March 9 | Section 4.2: Whitney's theorem | HW 6 due | |
Mon March 12 | Section 4.2: Menger's theorem | ||
Wed March 14 | Section 4.2: Fan lemma | Exam: 7pm in Talbot 103 (Topics) | |
Fri March 16 | No class | ||
Mon March 19 | Spring break: no class | ||
Wed March 21 | |||
Fri March 23 | |||
Mon March 26 | Chapter 4 Network Flows |
Section 4.3: Network flows | |
Wed March 28 | Section 4.3: The min-cut max-flow theorem | Infinite Loops | |
Fri March 30 | Section 4.3: Corollaries of min-cut max-flow | HW 7 due | |
Mon April 2 | Chapter 6 Planar Graphs |
Section 6.1: Planar graphs; Euler's theorem | |
Wed April 4 | Section 6.1: Special classes of planar graphs | ||
Fri April 6 | Section 6.2: Conditions for planarity | HW 8 due | |
Mon April 9 | Section 6.2: Conflict graphs | ||
Wed April 11 | Section 6.3: Map coloring | ||
Fri April 13 | No class | ||
Mon April 16 | Chapter 5 Coloring |
Section 5.1: Basic results | HW 9 due |
Wed April 18 | Section 5.1: Brooks's theorem | Exam: 7pm in Eng. Hall 106B8 (Topics) | |
Fri April 20 | Section 5.2: The Mycielskian | ||
Mon April 23 | Section 5.2: Color-critical graphs | ||
Wed April 25 | Section 5.3: The chromatic polynomial | ||
Fri April 27 | Chapter 7 Cycles |
Section 7.1: Edge chromatic number | HW 10 due. Vizing's refs: [1], [2], [3], [4] |
Mon April 30 | Section 7.2: Hamiltonian cycles; tough graphs | ||
Wed May 2 | Section 7.2: Hamiltonian cycles; Dirac's theorem | Not HW 11 | |
Mon May 7 | Final Exam 1:30-4:30pm in 245 Altgeld Hall (Topics) |