Graph Theory
Reinhard Diestel
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Kuratowski's theorem shows that a graph is planar if and only if it does not contain \(K_5\) nor \(K_{3,3}\) as a minor. We will study the notion of minors and topological minors of a graph and see various families of graphs that are characterized by certain forbidden minors. Then we will move our attention to graph colouring and see how mathematicians struggled and conquered the famous four color theorem. In the end, we will go deeper into graph minors and study tree-width, tangle, the graph minor theorem, and so on.
30% Homework + 20% Presentation + 25% Midterm1 + 25% Midterm2
There are 15 homework assignments. No quizzes. The deadline of each assignment is on Tuesday 2:00 pm one week after it was assigned. You have to use the \(\LaTeX\) template provided to type your homework and submit your homework through NSYS Cyber University.
Each homework assignment will list some questions for you to ponder. On each Tuesday class (and possibly other time), we will have a discussion on these questions. You may collect points accumulatively by answer these questions.
Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me.
Percentage scores will be converted to letter grades according to the university-wide standard table.
You are expected to attend the classes.
If you miss some course components due to illness, accident, family affliction, or religious observances, please talk to me and provide the documentation. In such cases, the course component is excused, and your course score will be calculated by distributing the weight of the missed item(s) across the other course components. Missing components are limited to at most 20%.
Do not copy others' work, including others' homework, the textbook, online materials, and others' answers in an exam; if it is really necessary, add proper citations to your references. It makes no point (and gives you no point) if the work is not yours since you learned nothing.