# Course description

The course will be concerned with topics in classical and modern graph theory:

- Properties of trees, cycles, matching, factors
- Forbidden subgraphs
- Planar graphs
- Graph colorings
- Random graphs
- Ramsey theory
- Graph minors

## Objectives

The class is oriented towards problem solving. The goal of the course for the students is to gain knowledge about the fundamental concepts in graph theory, solve interesting problems, learn how to write and present the proofs creatively.

## Prerequisites

Basic knowledge of linear algebra; appropriate for students starting from 5th semester.

# Examination

## Problem sheets

- Problem sheet 1: ( pdf ); Solutions: ( pdf ).

- Problem sheet 2: ( pdf ); Solutions: ( pdf ).

- Problem sheet 3: ( pdf ); Solutions: ( pdf ).

- Problem sheet 4: ( pdf ); Solutions: ( pdf ).

- Problem sheet 5: ( pdf ); Solutions: ( pdf ).

- Problem sheet 6: ( pdf ); Solutions: ( pdf ).

- Problem sheet 7: ( pdf ); Solutions: ( pdf ).

- Problem sheet 8: ( pdf ); Solutions: ( pdf ).

- Problem sheet 9: ( pdf ); Solutions: ( pdf ).

- Problem sheet 10: ( pdf ); Solutions: ( pdf ).

- Problem sheet 11: ( pdf ); Solutions: ( pdf ).

- Problem sheet 12: ( pdf ); Solutions: ( pdf ).

- Problem sheet 13: ( pdf ); Solutions: ( pdf ).

- Problem sheet 14: ( pdf ); Solutions: ( pdf ).

A problem sheet will be published here every Wednesday (starting on October 16) with 4 problems for 5 points each. **The due date is Wednesday the following week at 10:50 am.**

**Rules of submission:**

- In each paper that you submit, you shall leave a right margin of width at least 1/3 of the paper so that the tutors have enough space to write their comments.

- The submitted pages must be stapled together with the cover sheet, and your name(s) must be written in capital letters. You can find the cover sheet here.

- The problems are solved and solutions are submitted by
**individual students or pairs of students**. If you plan on specializing in Discrete Mathematics, then we advise you to submit your solutions individually.

- Every submission shall contain the solution to
**at most three problems**.

- When submitting in pairs, each student shall write
**at least one solution**.

- You can write your solutions either in English (preferable) or in German.

- You shall submit your solutions in a green box labeled "Graph Theory" in the atrium of the math building (20.30).

## Bonus

There is the possibility to obtain a bonus by successfully working the exercise sheets.

In order to receive the bonus you need to obtain **at least half of the total amount** of points on the **first 6 sheets, as well as on the second 6 sheets** (i.e., you need to receive at least 45 points on the first 6 sheets, and at least 45 points on the second 6 sheets).

The bonus will improve the grade of a **passed** exam of this lecture at the end of the semester by **one step** (0.3 or 0.4).

## Written exam

- The exam will take place on
**21.02.2020** from **8:00-12:00**.

# References

The main source is the book *Graph Theory* by Reinhard Diestel. The English edition can be read for free on the author’s web site (http://diestel-graph-theory.com/).

## Additional literature

- D. West --
*Introduction to graph theory* - B. Bollobás --
*Modern graph theory* - A. Bondy and U.S.R. Murty --
*Graph Theory* - L. Lovász --
*Combinatorial problems and exercises* - G. Chartrand, L. Lesniak and P. Zhang --
*Graphs & Digraphs*

## Lecture notes

There are lecture notes containing all relevant definitions, notation and theorems from the lecture. The first set of lecture notes contains full proofs, while the short version only contains definitions and statements of theorems.

- lecture notes: ( pdf | last updated on 31.01.2020)

- lecture notes (short version): ( pdf | last updated on 07.02.2020)