FI:MA010 Graph Theory - Course Information
MA010 Graph TheoryFaculty of Informatics
- Extent and Intensity
- 2/1. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
- prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
doc. RNDr. Jan Bouda, Ph.D. (seminar tutor)
RNDr. Robert Ganian (seminar tutor)
- Guaranteed by
- prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science - Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
- Wed 8:00–9:50 D3
- Timetable of Seminar Groups:
MA010/01: each odd Thursday 8:00–9:50 B007, J. Bouda
MA010/02: each even Thursday 8:00–9:50 B007, J. Bouda
MA010/03: each odd Friday 14:00–15:50 B011, R. Ganian
MA010/04: each even Friday 14:00–15:50 B011, R. Ganian
MA010/05: each even Friday 12:00–13:50 B011, R. Ganian
- ! PřF:M5140 Graph Theory &&! NOW ( PřF:M5140 Graph Theory )
Basic mathematics, sets, relations, induction (roughly corresponding to the mathematical parts of IB000).
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 180 student(s).
Current registration and enrolment status: enrolled: 0/180, only registered: 0/180, only registered with preference (fields directly associated with the programme): 0/180
- fields of study / plans the course is directly associated with
- there are 23 fields of study the course is directly associated with, display
- Course objectives
- This is a standard course in graph theory.
Basic concepts, graph properties, formulations of usual graph problems, and simple efficient algorithms for their solving, are presented. Although the content of this course is targetted at CS students, it is accessible also to others.
At the end of the course, successful students shall understand in depth and tell all the basic terms of graph theory; be able to reproduce the proofs of some fundamental statements on graphs; be able to solve new simple problems; and be ready to apply this knowledge in (especially) computer science applications.
- Graphs and relations. Subgraphs, isomorphism, degrees, implementation. Directed graphs.
- Graph connectivity, algorithms for searching. Multiple connectivity, edge-connectivity. Eulerian graphs.
- Distance in graphs, Dijkstra's algorithm, graph metric and its computation.
- Trees and their characterizations, tree isomorphism, rooted trees.
- Greedy algorithm. Spanning trees, MST problem. Algorithms of Jarnik and Boruvka. Matroids.
- Network flows: formulation and applications to practical problems. Ford-Fulkerson's algorithm for maximal flow. Applications to matching and representatives.
- Graph colouring, bipartite graphs and their recognition. Independence, cliques, vertex cover, relevant hard algorithmic problems.
- Planar embeddings of graphs, Euler''s formula and its applications. Planar graph colouring. Crossing numbers.
- Selected advanced topics (time allowing): Intersection graph representations, chordal graphs, structural width measures, graph minors, embedding on surfaces and planar covers, graph drawing - "spring embedder", some Ramsey theory.
- MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Invitation to discrete mathematics. 2nd ed. Oxford: Oxford University Press, 2009. xvii, 443. ISBN 9780198570431. info
- MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. Vyd. 2., opr. Praha: Karolinum, 2000. 377 s. ISBN 8024600846. info
- MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Invitation to discrete mathematics. Oxford: Clarendon Press, 1998. xv, 410. ISBN 0198502087. info
- Teaching methods
- MA010 is taught weekly 2-hour lectures, with bi-weekly 2-hour compulsory tutorials. Since this is a mathematical subject, the students are expected to learn the given theory and be able to understand and compose mathematical proofs. Memorizing is not enough! All the study materials, demonstrations, and study agenda are presented through the online IS syllabus.
- Assessment methods
- The resulting grade is taken from a term test (20%), voluntary bonus work (arbitrary), and a final written exam (80%). The written semester test for 20 points can be repeated (corrected) once, and at least 10 point score is strictly required before the final exam. Possible bonus points and penalties for not attending the compulsory tutorials count towards this limit. The final written exam for 80 points consists of a 40 point part about basic graph terms and their applications, and a 40 point advanced part in which students have to come with solutions and proofs of rather difficult problems. More then 50 points in total is required to pass.
- Language of instruction
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
- Listed among pre-requisites of other courses
- Teacher's information