# Course Identification

## Lecturers and Teaching Assistants

## Course Schedule and Location

## Field of Study, Course Type and Credit Points

## Comments

## Prerequisites

## Restrictions

## Language of Instruction

## Attendance and participation

## Grade Type

## Grade Breakdown (in %)

## Evaluation Type

**Examination**

## Scheduled date 1

## Scheduled date 2

## Estimated Weekly Independent Workload (in hours)

## Syllabus

We will cover a subset of the following. Basic definitions and parity arguments, Sperner's lemma; Borsuk-Ulam theorem; Hamilton and Euler circuits; trees: Cayley's theorem and the matrix-tree theorem; Flows and matchings: mincut-maxflow, Hall's theorem, Tutte's theorem; Connectivity: Menger. ; Planarity, Euler's formula. Applications to combinatorial geometry; Extremal graph theory: Turan's theorem, Erdos-Stone, Szemeredi's Regularity Lemma and applications; Random graphs and applications. Algebraic graph theory and spectral graph theory.

## Learning Outcomes

Upon successful completion of this course students should be able to:

[1] Describe the basic notions of graph theory.

[2] Discuss many of the elements of the cutting edge of modern research in the field of graph theory.

[3] Demonstrate familiarity with some striking examples of the applications of graph theory in topology, number theory, combinatorial geometry and other fields.