Entry requirements

30 credits in mathematics. Participation in Linear Algebra II. Participation in Probability and Statistics or Probability Theory I.

Learning outcomes

On completion of the course, the student should be able to:

• 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. Erdös-Rényi random graphs. Szemerédi´s regularity lemma. Infinite graphs. Applications in computer science. Extremal graph theory.

Instruction

Lectures, lessons and problem solving sessions.

Assessment

Written examination at the end of the course (2 credits). Assignments (3 credits) 

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.