Math 442 - 201, 2017WT2, Jan-Apr 2018

Optimization in Graphs and Networks


Announcements will be posted here from time to time. Please check regularly.
  1. Midterm details now up!
  2. Don't forget UBC will be closed February 12th, so no office hours that day. Please email me instead.
  3. Congratulations on your midterm average of 80%! Enjoy your candy!
  4. Here is the link to the Youtube video about the 4 colour theorem - thanks to Kristian for sharing it.
  5. Don't forget UBC will be closed April 2nd, so no office hours that day. Please email me instead.
  6. The course will be complete April 5th, so no office hours at 4pm.
  7. Max-flow min-cut was inspired by the Cold War. Thank you to Eric for this lead. Here is a blog post with references.

Lecture details

Lecturer: S van Willigenburg, Math 208, 822-2630, steph at math splotch ubc splotch ca.
Location:  TTh 14.00-15.30  CHEM C124.
Web page:
Office hours: Mon 10-11am, Thur 4-5pm, 15 mins just after class, and by appointment (not Wednesday). You can also email me anytime.

Course description

This is an introduction to graph theory. There will be emphasis both on proof and algorithmic techniques. Topics include tours and graphs, planarity, graph colouring, trees, shortest paths, flows, matchings.  Prerequisite is Math 340.


Robin J Wilson, Introduction to Graph Theory (5th Edition), Pearson. ISBN-13: 978-0-273-72889-4.  This text is optional and contains sketches of some of the proofs plus additional practice exercises. Other books on the subject can also be found in the library around QA 166.


There will be a weekly homework assignment due on Thursdays at the start of class. The homework is the most important part of the course as most of your learning will take place while doing it.   We will not accept late homework except in very unusual circumstances. We will, however, drop the lowest homework grade.


Midterm, Tuesday 6th February.
Final exam, Thursday 19th April.

Calculators, books, notes etc are not permitted in either exam. Please bring your student ID to both exams.

Please note that there are no make-up or alternate exams, so make sure you do not make travel plans, work plans etc that will conflict. Valid documentation must be provided within 72 hrs if any consideration is to be taken for a missed midterm.


Your grade will be based on the homework (10%), the midterm (30 or 40%), and the final (60 or 50%), whichever gives you the best grade.

Since this is a Mathematics Majors course, there is a median grade of around 68% and students will be expected to perform calculations and construct rigorous proofs involving fundamental ideas of the course.

Working together and academic integrity

Homework: We have no objection to collaboration on the homework, provided that it is done in a way that maximizes the benefit of the homework to all people involved. It is our experience that you get Regardless of whether you arrive at solutions in collaboration with others or alone, the paper that you turn in with your name on it should represent your own solutions, written in your own words.

In particular, you may not simply copy someone else's homework and turn it in as your own. Similarly, copying solutions that you might find on the web or from some other source is illegal.

These will all be treated as a violation of UBC's Academic Integrity Code. We take academic integrity very seriously and will follow university procedures in all cases of suspected cheating - disciplinary measures can result in expulsion.

Exams: There is anecdotal evidence that quite a bit of cheating occurs on campus. In an effort to prevent one common form of cheating, we will xerox a random sample of exam books before returning them.

Class etiquette

Use of cell phones (in any manner), laptops, smartphones, tablets and other electronic devices during class is highly inappropriate, as it is distracting and disrespectful to fellow students and the instructor. Chatting with neighbours, even when whispered, is equally inappropriate. If you have a question then please ask the instructor so the whole class may benefit too.

Arriving late and leaving early is also discouraged. If it happens then please enter/leave the room silently and do not disrupt the other students or instructor. Thank you.


Assignment 1, due Thursday January 4th.
Assignment 2, due Thursday January 11th.
Assignment 3, due Thursday January 18th.
Assignment 4, due Thursday January 25th.
Assignment 5, due Thursday February 1st.
No assignment due Thursday February 8th due to midterm.
Assignment 6, due Thursday February 15th.
Assignment 7, due Thursday March 1st.
Assignment 8, due Thursday March 8th.
Assignment 9, due Thursday March 15th.
Assignment 10, due Thursday March 22nd.
Assignment 11, due Thursday March 29th.
Assignment 12, due Thursday April 5th.


These are to help you study. Please make sure your solutions include full details and citations.

Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12

Other handouts

Here are some more study materials I found to help, or might be interesting.

Other useful links