Graph Theory

5 credits

Syllabus, Bachelor's level, 1MA170

A revised version of the syllabus is available.
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Grading system
Pass with distinction, Pass with credit, Pass, Fail
Finalised by
The Faculty Board of Science and Technology, 30 August 2018
Responsible department
Department of Mathematics

Entry requirements

35 credits in mathematics including Linear Algebra II and Probability and Statistics or Probability Theory I.

Learning outcomes

On completion of the course, the student should be able to:

  • know some important classes of graph theoretic problems;
  • be able to formulate and prove central theorems about trees, matching, connectivity, colouring and planar graphs;
  • be able to describe and apply some basic algorithms for graphs;
  • be able to use graph theory as a modelling tool.


Basic graph theoretical concepts: paths and cycles, connectivity, trees, spanning subgraphs, bipartite graphs, Hamiltonian and Euler cycles. Algorithms for shortest path and spanning trees. Matching theory. Planar graphs. Colouring. Flows in networks, the max-flow min-cut theorem. Random graphs. Structural properties of large graphs: degree distributions, clustering coefficients, preferential attachment, characteristic path length and small world networks. Applications in biology and social sciences.


Lectures, lessons and problem solving sessions.


Written examination at the end of the course combined with written assignments during the course according to instructions at course start.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.