Syllabus
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
Annotation
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 (