Math 3322: Graph Theory (Fall 2024)
General Information
Instructor: Mikhail Lavrov
Location: Mathematics 120
Lecture times: 3:30pm to 4:45pm on Tuesday and Thursday.
Office hours: 12:00pm to 2:00pm on Wednesday.
D2L page: https://kennesaw.view.usg.edu/d2l/home/3287990.
D2L will be used to submit assignments (these will be posted both here and on D2L, for convenience) and to view grades. The syllabus will also be posted there.
During the scheduled office hours, you should feel free to show up with no notice if you have questions of any kind.
If you cannot make the scheduled office hours, begin by emailing me; if your questions are easy to answer by email, I will do that, and if not, we can find another time to meet. (Allow some time for me to check my email.)
Homework and Exams
There will be eight homework assignments, two midterm exams, and one final exam; the dates are marked below.
I will post the homework assignments here and on D2L; they are always due on Friday at 11:59pm, via D2L.
Exams will be given in person during our ordinary 75-minute class period.
Textbooks
There is no official textbook for this course. I will publish lecture notes on this page before each class; all the material covered will be in those lecture notes.
If you would like additional references, I recommend the following:
- Chartrand and Zhang, A First Course in Graph Theory. This textbook is used by many other sections of Math 3322 (so some of you may already have it); it is also an inexpensive paperback.
- West, Introduction to Graph Theory. This is a very comprehensive resource, going into much more detail than we will on many topics. If you are reading it, read it slowly and carefully: a single page often corresponds to 10-15 minutes of class time!
Detailed Schedule
I will use the labels CZ and W to indicate which sections of the textbooks I mentioned above will correspond to which day of class. (We might not always cover everything in those sections, especially in W.)
The schedule below has links to lecture notes for every day of the semester, so that you can read ahead if you like. These will be updated as we go, and I will keep a log of the changes I make.
You may also be interested in an index to these notes, which is a list of key terms from graph theory, together with the lecture in which they are defined.
Note 9/27: Due to the day we missed on account of weather, we'll have one fewer lecture, and I've decided to skip tournaments (originally scheduled for lecture 19) to fit in the rest of the material. To make life easier on my end, I will not change the numbers of lectures 20-28. If you are interested in the missed content, you can still read it here.
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DateTopic CoveredOther details
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Tue 8/13Introduction to graphs
Lecture notesCZ 1.1, W 1.1 -
Thu 8/15Connected components
Lecture notesCZ 1.2, W 1.2 -
Tue 8/20Proof techniques
Lecture notesW App. 3 -
Thu 8/22Types of graphs
Lecture notesCZ 1.3, W 1.1-1.2
HW 1 due Friday -
Tue 8/27Proofs by induction
Lecture notesW App. 3 -
Thu 8/29The degree of a vertex
Lecture notesCZ 2.1, W 1.3 -
Tue 9/3Regular graphs
Lecture notesCZ 2.2, W 1.3 -
Thu 9/5Graphic sequences
Lecture notesCZ 2.3, W 1.3
HW 2 due Friday -
Tue 9/10Isomorphic graphs
Lecture notesCZ 3.1, W 1.1 -
Thu 9/12Trees and spanning trees
Lecture notesCZ 4.1, W 2.1 -
Tue 9/17Properties of trees
Lecture notesCZ 4.2, W 2.1 -
Thu 9/19Cayley's formula
Lecture notesCZ 4.4, W 2.2
HW 3 due Friday -
Tue 9/24Exam 1
-
Thu 9/26Canceled due to weather
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Tue 10/1Bipartite matchings
Lecture notesCZ 8.1, W 3.1 -
Thu 10/3König's theorem
Lecture notesW 3.1-3.2
HW 4 due Friday -
Tue 10/8Matchings in general graphs
Lecture notesCZ 8.1, W 3.3 -
Thu 10/10Directed graphs
Lecture notesCZ 7.1, W 1.4 -
Tue 10/15Eulerian graphs
Lecture notesCZ 6.1, W 1.2 -
Thu 10/17Hamiltonian graphs
Lecture notesCZ 6.2, W 7.2
HW 5 due Friday -
Tue 10/22Planar graphs
Lecture notesCZ 9.1, W 6.1 -
Thu 10/24Planarity testing
Lecture notesCZ 9.1, W 6.2
HW 6 due Friday -
Tue 10/29Polyhedra
Lecture notesW 6.1 -
Thu 10/31Exam 2
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Tue 11/5Cliques and independent sets
Lecture notesW 3.1, 5.1 -
Thu 11/7Vertex coloring
Lecture notesCZ 10.2, W 5.1
HW 7 due Friday -
Tue 11/12Bounds on chromatic number
Lecture notesW 5.1 -
Thu 11/14Cut vertices
Lecture notesCZ 5.1, W 4.1 -
Tue 11/19k-connectivity
Lecture notesCZ 5.3, W 4.2 -
Thu 11/21Menger's theorem
Lecture notesCZ 5.4, W 4.2
HW8 due Friday -
Thu 12/5Final exam (3:30pm to 5:30pm)