SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Topological and geometric graphs - NDMI095
Title in English: Topologické a geometrické grafy
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
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, Czech
Teaching methods: full-time
Additional information:
Guarantor: Mgr. Jan Kynčl, Ph.D.
doc. RNDr. Pavel Valtr, Dr.
Class: DS, diskrétní modely a algoritmy
Informatika Mgr. - Diskrétní modely a algoritmy
Kombinatorická geometrie a geom. algorit
Classification: Informatics > Discrete Mathematics
Annotation -
Last update: T_KAM (21.04.2016)
A drawing of a typical graph in the plane usually contains many crossings. A topological graph is a drawing of a graph in the plane where crossings of edges are allowed, including multiple crossings of the same pair of edges. A geometric graph is a special case where the edges are drawn as straight-line segments. Finding a drawing of a graph minimizing the number of crossings is a typical problem in this area. Various extremal problems are also studied, for example the maximum number of edges of a geometric graph with no k disjoint edges. Basic knowledge of graph theory and discrete geometry (
Literature -
Last update: Mgr. Jan Kynčl, Ph.D. (19.02.2019)

mostly research papers, a part covered by lecture notes; see for details

Requirements to the exam -
Last update: Mgr. Jan Kynčl, Ph.D. (19.02.2019)

The exam will be oral based on the material that was presented.

Syllabus -
Last update: Mgr. Jan Kynčl, Ph.D. (06.02.2019)

The Hanani--Tutte theorem and an algebraic algorithm for planarity testing

The Jordan curve theorem


Topological and geometric graphs without forbidden substructures

Complete topological graphs

Possibly other topics

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