MM856: Graph theory

Comment

MM855 is taught as part of MM856, and one can therefore only sign up for one of these courses.

Entry requirements

MM856 is taught as part of MM855, and one can therefore only sign up for one of these courses.

Otherwise no further 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

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Autumn

Tests

Mandatory assignments and written exam

EKA

N310057102

Censorship

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

Allowed(Except internet). A closer description of the exam rules will be posted under 'Course Information' on Blackboard.

ECTS value

Additional information

The final grade is based of an overall assesment (Mandatory assignment 20 % and written exam 80 %).

The examination form for re-examination may be different from the exam form at the regular exam.

Indicative number of lessons

90 hours per semester

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.
Total = 90 hours.

Activities during the study phase: To study the course material and prepare for the weekly exercises, individually or through group work.

Teacher responsible

Name	E-mail	Department
Anders Yeo	yeo@imada.sdu.dk	Institut for Matematik og Datalogi, Matematik

Timetable

31	Monday 02-08-2021	Tuesday 03-08-2021	Wednesday 04-08-2021	Thursday 05-08-2021	Friday 06-08-2021
08 - 09
09 - 10
10 - 11
11 - 12
12 - 13
13 - 14
14 - 15
15 - 16

Show full time table

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration & Legality

NAT

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