MA010 Graph Theory

Faculty of Informatics
Autumn 2024
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Daniel Kráľ, Ph.D., DSc. (lecturer)
Igor Balla, PhD (lecturer)
Bc. Filip Kučerák (seminar tutor)
Mgr. Xichao Shu (seminar tutor)
RNDr. Kristýna Pekárková (assistant)
Guaranteed by
prof. RNDr. Daniel Kráľ, Ph.D., DSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Daniel Kráľ, Ph.D., DSc.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Tue 24. 9. to Tue 10. 12. Tue 10:00–11:50 A217
  • Timetable of Seminar Groups:
MA010/01: Wed 2. 10. to Wed 11. 12. each even Wednesday 8:00–9:50 A217, F. Kučerák
MA010/03: Thu 3. 10. to Thu 12. 12. each even Thursday 14:00–15:50 B411, X. Shu
Prerequisites
! PřF:M5140 Graph Theory &&!NOW( PřF:M5140 Graph Theory )
Discrete mathematics. IB000 (or equivalent from other schools) is recommended.
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 200 student(s).
Current registration and enrolment status: enrolled: 34/200, only registered: 0/200, only registered with preference (fields directly associated with the programme): 0/200
fields of study / plans the course is directly associated with
Course objectives
This is a standard introductory course in graph theory, assuming no prior knowledge of graphs. The course aims to present basic graph theory concepts and statements with a particular focus on those relevant in algorithms and computer science in general. Selected advanced graph theory topics will also be covered. Although the content of this course is primarily targeted at computer science students, it should be accessible to all students.
Learning outcomes
At the end of the course, students shall understand basic concenpts in graph theory; be able to reproduce the proofs of some fundamental statements in graph theory; be able to solve unseen simple graph theory problems; and be ready to apply their knowledge particularly in computer science.
Syllabus
  • Basic graph theory notions: graphs, subgraph, graph isomorphism, vertex degree, paths, cycles, connected components, directed graphs.
  • Trees, Hamilton cycles, Dirac’s and Ore’s conditions.
  • Planar graphs, duality of planar graphs, Euler's formula and its applications.
  • Graph coloring, Five Color Theorem, Brooks’ Theorem, Vizing’s Theorem.
  • Interval graphs, chordal graphs, and their chromatic properties.
  • Vertex and edge connectivity.
  • Matchings in graphs, Hall’s Theorem.
  • Ramsey's Theorem.
  • Selected advanced topics (to be chosen from): Graph minors, graph embeddings on surfaces, planarity testing, list coloring, Tutte’s Theorem, Cayley’s formula.
Literature
    recommended literature
  • DIESTEL, Reinhard. Graph theory. 4th ed. Heidelberg: Springer, 2010, xviii, 436. ISBN 9783642142789. info
  • BONDY, J. A. and U. S. R. MURTY. Graph theory. [New York, N.Y.]: Springer, 2008, xiv, 657. ISBN 9781846289699. info
  • http://diestel-graph-theory.com/
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. 3., upr. a dopl. vyd. V Praze: Karolinum, 2007, 423 s. ISBN 9788024614113. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
Teaching methods
MA010 is taught in weekly 2-hour lectures, which are primarily focused on introducing the material (concepts, statements, proofs). The lectures are complemented with bi-weekly 2-hour tutorials where examples and problems related to the material presented during the lectures are made available to practice.
Assessment methods
The resulting grade will based on the final written exam. To register for the exam, it is necessary to obtain at least 16 points, which can be obtained for solving homework assignments; the homework assignments will have deadlines during the term.
Language of instruction
English
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
https://www.fi.muni.cz/~dkral/ma010.html
Basic information regarding course curriculum and examination can be found in the online syllabus MA010 in the Information System - "https://is.muni.cz/auth/el/1433/podzim20**/MA010/index.qwarp". More detailed information can be found on the course webpage maintained by the lecturer.

Since 2020, the grade is determined by the final exam only.

Since 2016, grading of MA010 changes by including a written homework assignment worth 20% and decreasing the weight of the final exam to 60%.

Since 2009, MA010 is taught in English. Předmět MA010 je od roku 2009 vyučován primárně anglicky. Informace v angličtině mají přednost, české materiály jsou doplňkové.

The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2024/MA010