Basic concepts of graph theory: degree, distance, diameter, matching etc. Theory for matchings, in particular for bipartite graphs. Structure theorems about 2- and 3- connected components of graphs, also Mader’s and Menger’s Theorems. Theory about minors, planarity. Coloring of various kinds, Perfect graphs, Hadwiger’s conjecture, random graphs and the probabilistic method.
SF2740 Graph Theory 7.5 credits
Information per course offering
Information for Autumn 2025 Start 25 Aug 2025 programme students
- Course location
KTH Campus
- Duration
- 25 Aug 2025 - 12 Jan 2026
- Periods
- P1 (3.7 hp), P2 (3.8 hp)
- Pace of study
25%
- Application code
50365
- Form of study
Normal Daytime
- Language of instruction
English
- Course memo
- Course memo is not published
- Number of places
Places are not limited
- Target group
Elective for all programmes as long as it can be included in your programme.
- Planned modular schedule
- [object Object]
- Schedule
- Schedule is not published
Contact
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus SF2740 (Spring 2022–)Headings with content from the Course syllabus SF2740 (Spring 2022–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
After the course the student should be able to
- explain basic concepts. theorems and proofs within the parts of graph theory described by the course content,
- use basic concepts. methods and theorems in graph theory to solve problems and communicate with the help of mathematical language.
Literature and preparations
Specific prerequisites
English B / English 6
Completed basic course SF1610 Discrete Mathematics, SF1662 Discrete Mathematics, SF1679 Discrete Mathematics or SF1688 Discrete Mathematics.
Recommended prerequisites
Completed basic course in Discrete Mathematics.
Literature
You can find information about course literature either in the course memo for the course offering or in the course room in Canvas.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
A, B, C, D, E, FX, F
Examination
- TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.
Other requirements for final grade
Continuous examination with assignments and presentation of project.
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Main field of study
Mathematics
Education cycle
Second cycle