Typical course contents might include the following: Graphs, digraphs, paths and cycles: Eulerian and Hamiltonian graphs, connectivity, adjacency matrices. Applications: shortest path problem, critical path problem, Guan's postman problem, travelling salesman problem.

Trees: properties, counting trees, minimum connector problem and other applications.

Planar graphs, Kuratowski's theorem, Euler's V-E+F=2 theorem, dual graphs.
Vertex-colourings, edge-colourings, and face-colourings of graphs, chromatic polynomials, four-colour theorem.

Matching, Hall's marriage theorem, Menger's theorem, max-flow min-cut theorem and application to network flow problems.