# SF2740 Graph Theory 7.5 credits

### Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

## Application

### For course offering

Autumn 2023 Start 28 Aug 2023 programme students

### Application code

50454

Headings with content from the Course syllabus SF2740 (Spring 2022–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

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.

### 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.

### Equipment

No information inserted

### Literature

No information inserted

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

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.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### 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.

Mathematics

Second cycle