Research Group on Discrete Mathematics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 1.044

Institut für Algebra und Geometrie
Englerstr. 2
D-76131 Karlsruhe

Office hours:
Tu, Th, F 8:30-12:00

Tel.: +49 721 608 47412

Fax.: +49 721 608 46968

# Graph Theory (Winter Semester 2019/20)

 Lecturer: Prof. Dr. Maria Axenovich, Dr. Richard Snyder Lecture (0104500), Problem class (0104510) 4+2

#### NEWS

 21.9.2020 Graph Th. exam

• Grades are now posted on the bulletin board next to room 1.043. The grades listed are calculated including the homework bonus (if it was obtained).

 Lecture: Problem class: Monday 9:45-11:15 Grashof-Hörsaal Begin: 14.10.2019 Friday 14:00-15:30 SR 1.067 Wednesday 11:30-13:00 SR 1.067
 Lecturer Prof. Dr. Maria Axenovich Office hours: Mon. 13:00-14:00 Room 1.043 Kollegiengebäude Mathematik (20.30) Email: maria.aksenovich@kit.edu Dr. Richard Snyder Office hours: Room 1.045 Kollegiengebäude Mathematik (20.30) Email: richard.snyder@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

• 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/).