SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Graphs and counting - NDMI078
Title in English: Grafy a počty
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
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.
Literature -
Last update: JUDr. Dana Macharová (06.01.2009)

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


Stanley, Enumerative Combinatrics I, Cambridge University Press 1997.

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


notes (připravovaná skripta)

Requirements to the exam -
Last update: 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: JUDr. Dana Macharová (06.01.2009)

Algebraic structure of cycles and cuts of graphs

Duality of enumeration: MacWilliams' theorem

Connections with the Ising partition function

Equivalence of basic generating functions

Connections with a classic open problem of graph theory: does a cubic

graph without bridges have an exponential number of perfect matchings?

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