### Extremal Graph Theory (Winter Semester 2024/25)

- Lecturer: Dr. Arsenii Sagdeev
- Classes: Lecture (0124060), Problem class (0124070)
- Weekly hours: 2+1

Welcome to the course!

It consists of two parts dedicated to major **Ramsey** and **Turán-type** problems in modern Extremal Combinatorics.

In the first half, we will mainly deal with the following question:

*what is the maximum number of edges in an n-vertex graph that does not contain some forbidden subgraphs?*

More specifically, we will prove the theorems of Mantel, Turán, Erdos-Stone, Bondy-Simonovits!

In the second half, we will be looking for the *order in an arbitrary large structure.*

More specifically, we will prove the famous Ramsey theorem and study its hypergraph, canonical, induced, and linear variants.

You will learn how to use probabilistic method, stepping-up lemma, Szemerédi regularity lemma, dependent random choice, and much more!

Lectures are held **weekly** starting from the 24th of October.

Problem classes are held **biweekly** starting from the 28th of October.

Attendance and homework are not compulsory (no credits) but **highly recommended**!

Google form for anonymous message to the lecturer.

Schedule | ||
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Lecture: | Thursday 9:45-11:15 | 20.30 SR 2.67 |

Problem class: | Monday 8:00-9:30 | 20.30 SR 2.59 |

Lecturers | ||
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Lecturer, Problem classes | Dr. Arsenii Sagdeev | |

Office hours: Tuesday, 13:00-14:00 | ||

Room 1.045 Kollegiengebäude Mathematik (20.30) | ||

Email: |

# References

For the first part of the course:

- David Conlon's lecture notes on Extremal graph theory

For the second part of the course:

- David Conlon's lecture notes on Ramsey theory