### Graph Theory (Winter Semester 2015/16)

- Lecturer: Prof. Dr. Maria Axenovich
- Classes: Lecture (0104500), Problem class (0104510)
- Weekly hours: 4+2

# Second Try Exam

The results are now posted on the pin board between room 1.043 and room 1.044.

The post exam review takes place on Tuesday, October 18 at 2pm in room 1.045.

Schedule | ||
---|---|---|

Lecture: | Tuesday 11:30-13:00 | SR 1.066 / 1.067 |

Thursday 9:45-11:15 | SR 1.066 / 1.067 | |

Problem class: | Friday 8:00-9:30 | SR 1.066 / 1.067 |

Lecturers | ||
---|---|---|

Lecturer | Prof. Dr. Maria Axenovich | |

Office hours: Wed. 13:45-14:45 | ||

Room 1.043 Kollegiengebäude Mathematik (20.30) | ||

Email: maria.aksenovich@kit.edu | ||

Problem classes | Torsten Ueckerdt | |

Office hours: | ||

Room Kollegiengebäude Mathematik (20.30) | ||

Email: torsten.ueckerdt@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

- There will be a problem sheet every Tuesday (starting on October 20) with 4 problems for 5 points each.
- 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**. -
**Due date is Tuesday the following week at 2:00 pm.** - The problems can be submitted during the lecture or deposited in a box in the atrium of the math building.

## 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 22, 2016**

Place: **Tulla HS** and **Fritz-Haller HS**

Time: **13:00 -- 16:00**

### Registration

To register for the exam "Graph Theory" go to the student portal at https://studium.kit.edu.

**Registration opens** at 10.1.2016.

**Registration closes** at 15.2.2016.

### Day of exam

Each student reads up his seat and should be 10 minutes before the exam begins at his/her seat.

## Grading

The final grade for the course is calculated based on the points achieved in the written exam.

# 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. Bollobas --
*Modern graph theory* - A. Bondy and U.S.R. Murty --
*Graph Theory* - L. Lovasz --
*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)
- supplementary material for extremal functions: (pdf)
- supplementary material for hypergraph Ramsey: (pdf)

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)