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Graphs and counting - NDMI078

Title:	Grafy a počty
Guaranteed by:	Department of Applied Mathematics (32-KAM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Martin Loebl, CSc.
Class:	Informatika Mgr. - volitelný
Classification:	Informatics > Discrete Mathematics

Annotation -

Last update: JUDr. Dana Macharová (06.01.2009)

Discrete enumeration with applications in both graph theory and statistical physics.

Course completion requirements -

Last update: doc. Mgr. Jan Kynčl, Ph.D. (31.05.2019)

Oral exam.

Literature -

Last update: JUDr. Dana Macharová (06.01.2009)

Mohar, Thomassen, Graphs on surfaces, The Johns Hopkins University Press,

2001.

Stanley, Enumerative Combinatrics I, Cambridge University Press 1997.

Loebl, M.: Discrete mathematics and statistical physics; introductory

lecture

notes (připravovaná skripta)

Requirements to the exam -

Last update: doc. Mgr. Jan Kynčl, Ph.D. (24.05.2019)

For the main exam, the requirements correspond to the syllabus as covered by the lectures.

Syllabus -

Last update: prof. RNDr. Martin Loebl, CSc. (30.12.2020)

Algebraic structure of cycles and cuts of graphs

Duality of enumeration: MacWilliams' theorem

Connections with the Ising partition function

Equivalence of basic generating functions

Algorithmic aspects