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Research Group on Discrete Mathematics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 1.044

Address
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 2015/16)

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