Graph Theory

5 credits

Syllabus, Bachelor's level, 1MA170

A revised version of the syllabus is available.
Code
1MA170
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, 18 March 2010
Responsible department
Department of Mathematics

Entry requirements

Mathematics 35 credits including Linear Algebra II and Probability and Statistics

Learning outcomes

In order to pass the course the student should

  • 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.

Content

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.

Instruction

Lectures, lessons and problem solving sessions.

Assessment

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

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