# MM810: Graph Theory I

## Comment

## Entry requirements

## Academic preconditions

Students taking the course are expected to have knowledge of linear algebra, and basic notions and methods from abstract algebra.

## Course introduction

results from graph theory, which is important in regard to identify

mathematical structures from graph theory in concrete examples.

The

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:

- Give

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
- carry

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

## Content

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.

## Literature

## Examination regulations

## Exam element a)

## Timing

Autumn

## Tests

## Report and oral examination

## EKA

## Censorship

## Grading

## Identification

## Language

## Examination aids

To be announced during the course

## ECTS value

## Additional information

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

## Teaching Method

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.