MA052 Advanced Graph Theory II

Faculty of Informatics
Spring 2007
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), 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
Wed 9:00–11:50 B411
Prerequisites
Usual basic knowledge of discrete mathematics and graphs. (See the book "Invitation to discrete mathematics".) Some knowledge of algorithmic complexity.
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 8 fields of study the course is directly associated with, display
Course objectives
Structural graph theory is gaining more and more attention these days, mainly in connection with the Graph Minor Theory of Robertson and Seymour (which is one of the deepest results of discrete mathematics of all times). For instance, the theory implies existence of polynomial algorithms for many graph problems, sometimes even when it is not clear whether a problem is solvable at all.
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.
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 Minor Theorem, an outline.
  • Advanced width measures: clique-width, rank-width.
  • MS2- and MS1-theorems.
  • Extensions to structural matroid theory.
Literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
Assessment methods (in Czech)
Written individual homework assignment (one), and a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTS.html
The course is also listed under the following terms Spring 2009, Spring 2011, Spring 2013.
  • Enrolment Statistics (Spring 2007, recent)
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