Entry requirements

35 credits in mathematics including Linear Algebra II and Probability and Statistics or Probability Theory I.

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 combined with written assignments during the course according to instructions at course start.