# Geometric Graphs

Time and place: Wednesday 2:15-3:45 pm, Kémia 160 (Északi tömb, Pázmány Péter stny. 1/A).

The course had lectures by Dömötör Pálvölgyi, and from two invited guest Tóths.

Prerequisites:
Basic knowledge of graph theory (Kombinatorika 1/Végmat 1)

#### Some links:

Lovász: Graphs and Geometry (focus on Chapters 3 and 5)

Pach-Agarwal: Combinatorial Geometry (Chapter 14)

Graph Theory II (a course by Géza Tóth)

#### Exams:

You have to choose and learn 10-X from the below 12 topics, and present one of them (that I choose) orally.
(In this formula X was known as the number of correct homework assignments, but recently Musk acquired it.)
When: Some dates are in Neptun, but other times are also discussable, just email me when you would prefer to come!
#### Lectures:

Lecture 1: Geometric graphs (Wagner-Fáry), Drawing outerplanar graphs on any point set (Gritzmann, Mohar, Pach, Pollack)

Lecture 2: Drawing planar graphs on a grid (De Fraysseix, Pach, Pollack; Schnyder)

Lecture 3: Rubber band representation (Tutte), From polyhedra to graphs

Lecture 4: From graphs to polyhedra (Cremona-Maxwell): Steinitz's theorem, Circle packing theorems (Koebe-Andreev-Thurston), Cage theorem (Andreev)

Lecture 5: Separator theorem (Lipton-Tarjan), Segment intersection graphs (Pawlik et al.)

Lecture 6: Spanners

No class on October 25 and November 1!

Lecture 7 (November 8): Hanani-Tutte

Lecture 8 (November 15): Guest lecture by Csaba Tóth: Simple k-planar graphs

Lecture 9 (November 22): Crossing-lemma and applications: k-planarity, unit distances, halving lines

Lecture 10 (November 29): Guest lecture by Géza Tóth: Crossing number variants

Lecture 11 (December 6): Thrackles and related problems

No class on December 13 but you should watch the video! This counts as Lecture 12.