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.
Announced no later than 4 weeks before the start of the course on the course web page.
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
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