MM856: Graph theory
The Study Board for Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310057102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master
STADS ID (UVA): N310057101
ECTS value: 10
Date of Approval: 13-05-2020
Duration: 1 semester
Version: Approved - active
Entry requirements
Academic preconditions
Students taking the course are expected to have basic knowledge of graph theory and discrete mathematics, corresponding to the material in the course MM541 (Combinatorial Mathematics).
Course introduction
The aim of the course is to enable the student to review definitions and 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 course MM541, 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 complex scientific projects at a high level. This involves solving complex problems using tools from graph theory.
- 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.
- give coherent solutions, arguing why the individual steps hold.
- carry out complete proofs for results from the course curriculum.
- explain connections between results and concepts in graph theory.
- Use graph algorithms in order to solve complex problems.
Content
The following main topics are contained in the course: Graphs, trees, distances, matchings in general graphs, paths, cycles, colouring in graphs, Hamilton cycles, planar graphs, random graphs, NP-hardness and directed graphs.
Literature
Examination regulations
Exam element a)
Timing
Autumn and January
Tests
Portfolio and tests
EKA
N310057102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Duration
3 hours
Examination aids
All common aids are allowed e.g. books, notes and computer programmes which do not use internet etc.
Internet is not allowed during the exam. However, you may visit the course site in itslearning to open system "DE-Digital Exam". If you wish to use course materials from itslearning, you must download the materials to your computer no later than the day before the exam. During the exam you cannot be sure that all course materials is accessible in itslearning.
ECTS value
10
Additional information
Portfolio exam consisting of two parts:
- Compulsory assignments - weighted 20%
- Written examination (January) - weighted 80%
Indicative number of lessons
Teaching Method
The teaching method is based on three phase model.
- Intro phase (lectures, question classes): 52 hours.
- Skills training phase (exercise sessions): 38 hours.
Activities during the study phase: To study the course material and prepare for the weekly exercises, individually or through group work.