Topological and geometric graphs - NDMI095
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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 (
Last update: T_KAM (21.04.2016)
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Oral exam. Last update: Kynčl Jan, doc. Mgr., Ph.D. (29.05.2019)
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mostly research papers, a part covered by lecture notes; see https://kam.mff.cuni.cz/~kyncl/tgg/ for details Last update: Kynčl Jan, doc. Mgr., Ph.D. (19.02.2019)
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The exam will be oral based on the material that was presented. Last update: Kynčl Jan, doc. Mgr., Ph.D. (19.02.2019)
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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 Last update: Kynčl Jan, doc. Mgr., Ph.D. (06.02.2019)
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