MM810: Graph Theory I
Students taking the course are expected to have knowledge of linear algebra, and basic notions and methods from abstract algebra.
results from graph theory, which is important in regard to identify
mathematical structures from graph theory in concrete examples.
course builds on the knowledge acquired in the courses MM538, and gives
an academic basis for studying further topics with the intent to write a
thesis in discrete mathematics.
In relation to the competence profile of the degree it is the explicit focus of the course to:
the competence to plan and execute scientific projects at a high level,
and to manage work and development situations that are complex,
unpredictable and that require new solving skills.
- Give skills
to study, analyse, model and solve problems on a high level of
abstraction using logical and structured argumentation.
- Give knowledge about advanced models and methods in graph theory
Expected learning outcome
The learning objectives of the course are that the student demonstrates the ability to:
- review definitions and results from graph theory
- use the theory to solve concrete problems
- argue for the single steps in the solutions of problems
out complete proofs for results from the course curriculum (counting
arguments, induction, indirect proofs, algorithmic proofs)
- explain connections between results and concepts in graph theory
- use mathematical notation from set theory, function theory and logic
- identify mathematical structures from graph theory in concrete examples
The following main topics are contained in the course: Graphs, subgraphs, connected graphs, trees, nonseparable graphs, tree-search algorithms, complexity of algorithms, connectivity, stable sets and cliques, matchings, Hamilton cycles.
Exam element a)
Report and oral examination
To be announced during the course
The report is assessed as part of the oral examination.
The examination form for re-examination may be different from the exam form at the regular exam.
Indicative number of lessons
At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.
Activities during the study phase: To study the course material and prepare for the weekly exercises, individually or through group work.