Graph Theory (Math 180, Winter 2021)

Instructor: Igor Pak
See email instructions below.

Class schedule: MWF 9:00 - 9:50 am, LA time, online.

Zoom meeting link and password will be sent by email from the course my.ucla site.
They are also permanently displayed on the course CCLE website.

Discussion Section: Tue 9:00 - 9:50, online (address to be announced)

Office Hours: Mon 10:00-10:50 am (right after class), Mon 2:00-2:30 am (for other time zones), or by appointment.
For all these, use the course Zoom link.

Teaching Assistant: Jason Snyder (see that website for email)

TA Office Hours: Tue 10-11 am (regular), Fri 12-1 pm (open)

Discussions and TA OH Zoom meeting links are posted on the CCLE website.

Note: University deadlines and holidays according to the UCLA academic calendar.

Textbooks: J. Matousek, J. Nesetril (MN), Invitation to Discrete Mathematics, Oxford Univ Press, Second Edition
Online content (UCLA library)
MN Table of content (see also MN Amazon page)

Additional reading will be posted on this page if necessary.

Grading: Homeworks: 20%, Midterm: 20%, Final: 60%.

Difficulty: This is an introductory course in Graph Theory and related topics. The students are expected to learn the theory and solve problems on the homeworks. The problems will be both computational and require some proof abilities.

Other expectations: I would guess that the average student should spend about 8-10 hours per week outside of class to get a decent grade (incuding discussion sections and study group meetings). Much of this time should be spent on the homeworks, but some should be spent on reading the book and absorbing the class material.


We will cover most book sections covering Graph Theory. We will aim to adhere to the approximate timetable given on the Department website for the course.

Although much of the material will follow the textbook, I will change the order of sections and some additional material will be presented in class, so class participation is very important. More specific info on the order of sections will be posted soon.

Lecture notes and videos: The class will follow the book fairly closely, so I will not be making regular lecture notes. However, I will be making in-class Zoom videos available to accommodate students unable to join during the lecture. I expect students to view all lectures either in class or after hours. Occasionally, additional reading materials will be posted here (or on CCLE website if copyright restricted to UCLA students), as they come available.

Home Assignments

The weekly home assignments will be given on Wednesdays to be returned also on Wednesdays. No assignment will be given over the week before the midterm. Worst HA will be dropped from the final score. The assignments will be posted here (on the course web page) in .pdf format. The solutions will need to be uploaded to Gradescope, which is also linked to the course CCLE website.

HA1 is here, due Jan 13.

HA2 is here, due Jan 20.

HA3 is here, due Jan 27.

HA4 is here, due Feb 3.

No HA due Feb 10 -- Midterm! Consider using 2016 midterm as a practice test.

HA5 is here, due Feb 17.

HA6 is here, due Feb 24.

HA7 is here, due Mar 3.

HA8 is here, due Mar 10.

Midterm and Final Exams

There will be one in-class midterm and one final.

Midterm: Wed Feb 10, 2021, online, 24 hr window, exact times 8:00 am PT -- 7:59 am PT next day.

Midterm problems are available here.

Midterm answers:
1. 1260, 26208 (or, using the book's definition of P5, 169344), 0, 1980, 26208, 138600
2. 2308, not unique (if 610 used in place of 61 a correct solution is accepted)
3. 38610
4. 4, infinite

Final: Mon Mar 15, 2021, online, 24 hr window, exact times 8:00 am PT -- 7:59 am PT next day.

Practice final answers:
1. all edges (1,j') and (i,1'),
2. 94.5
3. Hint: number of spanning trees is at most |E|-choose-n, and |E| <3n.
4. Hint: use Euler's formula
5. Hint: d1 >2 because otherwise the graph is a union of at least two connected components which are paths
6. Hint: cliques give lower bound for the chromatic number
8. 112
9. Hint: use induction
10. TTTFT, T (n/6 typo) FT(we didn't cover that) T, F(we didn't cover that) FTTT

Collaboration Policy

For the home assignments (HA), you can form discussion groups of up to 3 people each. In fact, I would like to encourage you to do that. You can discuss problems but have to write your own separate solutions. You should write the list of people in you group on top of each HA.

Note: On CCLE, I opened a discussion forum where you can post replies in case you are looking for study partners.

Email Policy

To e-mail me click here and delete .zzz
Put Math 180 in the Subject line.
Please put in your first line "Dear Professor Pak," -- no other salutations are allowed in the first line of the message.
At the end of your email, you must include your full name, UCLA id, and your official email address (for privacy purposes). Replies will be send only to the UCLA address.

Click here to return to Igor Pak Home Page.

Last updated 3/13/2021