Course detail
Graphs and Algorithms
FSI-SGA-A Acad. year: 2025/2026 Winter semester
The course will provide students with basic concepts of the theory of graphs and with some algorithms based on that theory. After the basic definitions, the classic problems will be discussed including the Euler path and Hamilton cycle of a graph, vertex colouring, planar graphs etc. The next concept to be investigated will be trees and algorithms for a minimal spaning tree finding. Students will also learn about bipartite graphs, matching problem and shortest path problem. Direcdted graphs will also be discusses including algorithms for critical path finding. Finally, networks and flows in them will be deal with. The course will be oriented towards applications of graphs that can be found in many areas, particularly in technological sciences. Emphasis will be placed on applications in computer science, optimization, theory of control, and operation research.
Language of instruction
English
Number of ECTS credits
4
Supervisor
Department
Entry knowledge
Students are expected to have secondary school knowledge of set theory and combinatorics.
Rules for evaluation and completion of the course
The course unit credit is awarded on condition of having attended the seminars actively and passed a written test. The exam has a written and an oral part. The written part tests student's ability to deal with various problems using the knowledge and skills acquired in the course. In the oral part, the student has ro prove that he or she has mastered the related theory.
The attendance at seminars is required and will be checked systematically by the teacher supervising the seminar. If a student misses a seminar, an excused absence can be cpmpensated for via make-up topics of exercises.
Aims
The course aims to acquaint the students with the theory of graphs and graph-based algorithms, which are commonly used to solve problems in engineering and many other areas.
The students will be made familiar with the basics of the theory of graphs and graph algorithms. This will provide them with tools for using graphs to model various practical problems, which may then be solved by using the graph algorithms.
Study aids
The students may use the study texts provided by the subject supervisor that are placed at the web page of the Institute of Mathematics as files for downloading.
The study programmes with the given course
Programme N-MAI-A: Mathematical Engineering, Master's, compulsory
Programme N-MAI-P: Mathematical Engineering, Master's, compulsory
Programme N-LAN-A: Logistics Analytics, Master's, compulsory
Programme N-AIM-A: Applied and Interdisciplinary Mathematics, Master's, compulsory
Type of course unit
Lecture
26 hours, optionally
Syllabus
- Basic con cepts
- Walks, paths and, cycles
- Trees and spanning trees
- Vertex coloring
- Planarity
- Sorting algorithms
- Shortest path problem
- Edge colouring
- Bipartite graphs
- Sorting
- Directed graphs
- Critical path problem
- Flows and Networks
Exercise
13 hours, compulsory
Syllabus
Seminars will closely follow the lectures.