1. To solve homogeneous and non-homogeneous linear recursion.
2. Apply the recursive way of thinking on the appropriate combinatorial problems.
3. Describe and manipulate with basic notions from graph theory.
4. Describe and solve appropriate engineering problems in terms of graph theory.
5. Solve problems algorithmically using computers.

4 hours of lectures a week. The lecturer is going to follow the lecture materials.

During the semester 3 software excercises will be given to be solved by the students individually and to be shown in the framework of laboratory excercises.

1. Fibonacci's sequence; Homogeneous recursive relations.
2. Homogeneous recursive relations.
3. Non-homogeneous recursive relations.
4. Notion of a graph; Main definitions and examples; Graph isomorphism.
5. Connectivity; Paths; Eulerian and hamiltonian graphs; Optimization algorithms; Shortest path problem; Chinese postman problem; Travelling salesman problem.
6. Different characterizations of trees.
7. Labelled trees; Prüfer code; Minimum spanning tree; Algorithms.
8. Midterm exam.
9. Kuratowski's theorem; Euler's formula.
10. Dual graphs; Planarity testing algorithms.
11. Vertex colourings; Brooks' theorem; Edge colourings.
12. Face colourings of planar graphs; Four colour theorem.
13. Notion of a digraph; Connectivity and strong connectivity; Critical path problem; Algorithms; Tournaments.
14. Marriage problem; Hall's theorem; Transversals; Application to latin squares.
15. Final exam.