Subjects(version: 845)
Topological and geometric graphs - NDMI095
Title in English: Topologické a geometrické grafy Department of Applied Mathematics (32-KAM) Faculty of Mathematics and Physics from 2018 to 2018 summer 3 summer s.:2/0 Ex [hours/week] unlimited unlimited taught English, Czech full-time https://kam.mff.cuni.cz/~kyncl/tgg/
Guarantor: Mgr. Jan Kynčl, Ph.D.doc. RNDr. Pavel Valtr, Dr. DS, diskrétní modely a algoritmyInformatika Mgr. - Diskrétní modely a algoritmyKombinatorická geometrie a geom. algorit Informatics > Discrete Mathematics
 Annotation - ---CzechEnglish
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 - ---CzechEnglish
Last update: Mgr. Jan Kynčl, Ph.D. (19.02.2019)

mostly research papers, a part covered by lecture notes; see https://kam.mff.cuni.cz/~kyncl/tgg/ for details

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

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

 Syllabus - ---CzechEnglish
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

Thrackles

Topological and geometric graphs without forbidden substructures

Complete topological graphs

Possibly other topics

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