MA010 Graph Theory

Faculty of Informatics
Autumn 2019
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Jacob Cooper, Ph.D. (seminar tutor)
Robert Arthur Hancock, PhD (seminar tutor)
RNDr. Deniz Agaoglu Cagirici, Ph.D. (assistant)
Onur Cagirici, M.Sc., Ph.D. (assistant)
Guaranteed by
prof. RNDr. Petr Hliněný, Ph.D.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Fri 10:00–11:50 D3
  • Timetable of Seminar Groups:
MA010/01: each even Tuesday 8:00–9:50 C525, R. Hancock
MA010/02: each odd Tuesday 8:00–9:50 C525, R. Hancock
MA010/03: each even Wednesday 14:00–15:50 C525, J. Cooper
MA010/04: each odd Wednesday 14:00–15:50 C525, J. Cooper
Prerequisites
! PřF:M5140 Graph Theory &&!NOW( PřF:M5140 Graph Theory )
Discrete mathematics, basic concepts of graphs and of graph algorithms. IB000 (or equivalent from other schools) is highly 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: 1/200, 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
there are 26 fields of study the course is directly associated with, display
Course objectives
This is a standard course in graph theory, assuming little introductory knowledge of graphs. It aim is to present all usual basic concepts of graph theory, graph properties (with simplified proofs) and formulations of typical graph problems. This is also supplemented with some abstract-level algorithms for the presented problems, and with some advanced graph theory topics. Although the content of this course is primarily targeted at CS students, it is accessible also to others.
Learning outcomes
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 graph problems; and be ready to apply this knowledge in (especially) computer science applications.
Syllabus
  • Graphs and relations. Subgraphs, isomorphism, degrees. Directed graphs.
  • Graph connectivity and searching, multiple connectivity. Trees, the MST problem.
  • Distance in graphs, graph metrics, concepts of route planning in graphs.
  • Network flows. The "max-flow min-cut" theorem via Ford-Fulkerson's algorithm. Applications to connectivity and representatives.
  • Matching in graphs, packing problems, enumeration.
  • Graph colouring, properties, easy and hard cases. Edge and list colourings.
  • Drawings and planar graphs, duality, Euler's formula and its applications.
  • Computationally hard graph problems on graphs, how to tell "difficulty" of a graph problem.
  • Selected advanced topics (time allowing): Intersection graph representations, chordal graphs, structural width measures, graph minors, graph embeddings on surfaces, crossing number, Ramsey theory.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. 3rd ed. Berlin: Springer, 2006, xvi, 410s. ISBN 3540261834. info
    recommended literature
  • http://diestel-graph-theory.com/
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. 3., upr. a dopl. vyd. V Praze: Karolinum, 2007, 423 s. ISBN 9788024614113. info
Teaching methods
MA010 is taught in 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 semester test (20%), semester homework assignment (20%), optional bonus work (arbitrary), and a final written exam (60%). The written semester test can be repeated (corrected) once, and the homework assignment can also be rewritten once within the given limits. At least 20% points semester score is strictly required before attending the final exam. Possible bonus points and penalties for not attending the compulsory tutorials count towards this limit. The final written exam for 60% of points consists of a part testing basic graph notions and their applications, and an 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
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
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 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2019, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2019/MA010