MA052 Advanced Graph Theory II

Faculty of Informatics
Spring 2011
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Timetable
Thu 9:00–11:50 G124
Prerequisites
Graph theory MA010. Some knowledge of algorithmic complexity and of predicate logic is welcome.
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 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 19 fields of study the course is directly associated with, display
Course objectives
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, like tree-width or branch-width or rank-width.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Repetition of basic graph terms.
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications.
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • MS2- and MS1-theorems.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (a seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay, or more), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
http://is.muni.cz/el/1433/jaro2011/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2013.
  • Enrolment Statistics (Spring 2011, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2011/MA052