Examination

• Date: February 27 (Tuesday), 2007
• Time: 09:00-11:00 (2 hours)
• Place: IFW A36
• Details: [PDF] [PS]

Time & Place

• Lectures : Wednesday, 10-12 @ CAB G56.
• Exercises : Wednesday, 15-16 @ CAB G56.

Instructors

Lecturer: Tibor Szabó

CAB G31.2/ Tel: (044) 632-0858. e-mail: szabo@inf.ethz.ch

Assistant: Andreas Razen

CAB G37.1/ Tel: (044) 632-7422. e-mail: arazen@inf.ethz.ch

Abstract of the course

This course is an introduction to the theory of graphs intended for students in mathematics and computer science/engineering students with an interest in theory. We start from basic definitions and examples, but hope to move on quickly and cover a broad range of topics. Some applications and relations to Computer Science will also be discussed. Emphasis will be given to reading, understanding and developing proofs. There is no prerequisite, other than basic mathematics introduced in the Grundstudium. Possible topics include: degrees, paths, trees, cycles, Eulerian circuits, bipartite graphs, extremality, matchings, connectivity, network flows, vertex and edge colorings, Hamiltonian cycles and planarity.

Procedures, exam, exercises

In lecture we will follow the textbook "Introduction to Graph Theory" by Doug West. In the recitation we will sample from the great number of excellent exercises related to the topic of the current lecture. We do not require, but highly recommend that you try to solve all the homework exercises and if you do so, write them up. Writing up teaches you to precisely formulate your (maybe vague) ideas and communicate them such that others (in this case us) understand them. This ability is beneficial not just in mathematics but in (almost) any discipline. Whatever you write up we will read and comment on. Another reason to struggle with the homework problems is to prepare yourself for the final exam. Grading will solely be based on this two-hour, written exam, taking place in the Feb/March exam period following the course. Testat is given to those students who pass this exam.

Language

English (written, spoken, whatever)

Course material

Lectures	Transparencies (1-in-1 version)	Transparencies (4-in-1 version)	Problems	Misc.
Lecture 1 October 25 (Basics)	[PDF][PS]	[PDF][PS]	[PDF][PS]	[PDF][PS] <Welcome>
Lecture 2 November 1 (Basics II)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 3 November 8 (Extremal Problems)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 4 November 15 (Trees)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 5 November 22 (Matchings I)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 6 November 29 (Matchings II)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 7 December 6 (Connectivity I)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 8 December 13 (Connectivity II)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 9 December 20 (Coloring I)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 10 January 3 (Coloring II)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 11 January 10 (Coloring III)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 12 January 17 (Coloring IV)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 13 January 24 (Turán-Type Problems, Planar Graphs I)	[PDF][PS]	[PDF][PS]	[PDF][PS]
Lecture 14 January 31 (Planar Graphs II)	No new slides	No new slides	[PDF][PS]

Literature

• Douglas B. West, Introduction to Graph Theory (2nd edition), Prentice Hall, 2001.
• J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, 1976.

• B. Bollobás, Modern Graph Theory, Springer, 1998.
• R. Diestel, Graph Theory, Springer, 2000. (A German Edition is also available).

Links

• Robin Thomas's page on the new proof of the Four Color Theorem.
• Vasek Chvátal's page on the Strong Perfect Graph Theorem.
• Bjarne Toft's page on Graph Coloring Problems.
• Stephen Locke's page on Unsolved Problems.
• Douglas West's page on Open Problems.
• Dan Archdeacon's page on Problems in Topological Graph Theory.