PhD in Mathematics

Planar Graphs and Polyhedra

Planar Graphs and Polyhedra

Academic year 2024/2025

Sommario del corso

• Program
• Suggested readings and bibliography
• Notes
• Class schedule
• Teaching tools
• Course card

Program

A graph is the data of vertices (points) and edges (lines connecting the points). This course will focus on planar graphs, i.e.~those that can be drawn in the plane (or on the surface of a sphere) without any edge crossings, except at vertices. A special type of planar graphs are the $3$-polytopes (polyhedra), that are the planar, $3$-connected graphs (planar, and however we remove $0$, $1$ or $2$ vertices, the resulting graph is connected). We will cover the following topics: characterisation of maximal planar graphs (by the way these are a subclass of polyhedra), overview of Kuratowski's Theorem, statement of the Rademacher-Steinitz Theorem (characterising polyhedra), enumeration of polyhedra, Tutte's and related algorithms, graphical degree sequences, unigraphicity, characterisations of special subclasses of polyhedra. A few of the topics covered are at the cutting edge of research, and are related to interesting open problems in this area.

Bollobas : Modern Graph Theory (Springer).
Diestel : Graph Theory (Springer).

Notes

Hours: 15 Period: January - May 2025

Class schedule

• Teaching material
• Exams and finals
• Class schedule
• Go to Moodle
• Register for the course
• Enrolled students
• Invia email agli studenti registrati
• Export table