# Graph Theory (Winter Semester 2017/18)

Lecturer: | Prof. Maria Axenovich Ph.D., Mónika Csikós |
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Classes: | Lecture (0104500), Problem class (0104510) |

Weekly hours: | 4+2 |

Lecture: | Monday 14:00-15:30 | SR 1.067 |
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Wednesday 9:45-11:15 | SR 1.067 | |

Problem class: | Thursday 9:45-11:15 | Chemie-Hörsaal Nr. 2 (HS2) |

Lecturer | Prof. Maria Axenovich Ph.D. |
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Office hours: Mondays 15:40-16:40 | |

Room 1.043 Kollegiengebäude Mathematik (20.30) | |

Email: maria.aksenovich@kit.edu | |

Problem classes | Mónika Csikós |

Office hours: upon request | |

Room 1.039 Kollegiengebäude Mathematik (20.30) | |

Email: monika.csikos@kit.edu |

# 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

**Please register for the homework on this website.**

A problem sheet will be published here every Wednesday (starting on October 18) with 4 problems for 5 points each. **Due date is Wednesday the following week at 9:45 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 and your name has to be written on the front page with capital letters.

- The problems are solved and solutions are submitted by
**individual students or pairs of students**. - 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 blue 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**.

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

There will be a written exam at the end of semester on

Date: **February 27, 2018**

Place: **Johann-Gottfried-Tulla Hörsaal** and **Gaede-Hörsaal**

Time: **08:00 -- 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. However, they provide no proofs and only a few examples.

- lecture notes: ( pdf | last updated on 21 November )

There are notes taken by a student during the winter term 2011/12 containing the proofs. The current version is **not approved** and ** claims neither completeness nor correctness**.

- unrevised notes: (pdf)