## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Graph Theory WS 04-05

# Graph Theory (37-485) WS 04/05

## Examination

• Date: March 1 (Tuesday), 2005
• Time: 9:00 - 11:00 AM
• Place: HG D1.1 (Room D1.1 of the Main Building of ETH)
• Details: [PDF][PS]
• Administration: Mathematics students and graduate students, please send an email to us to tell whether you are going to take the exam or not.

## Time & Place

• Lectures: Wed 10-12 @ IFW B42.
• Exercises: Wed 15-16 @ IFW B42.

## Instructors

Lecturer: Tibor Szabó
IFW B48.1/ Tel: (01) 632-0858. e-mail: szabo@inf.ethz.ch

Assistant: Milos Stojakovic
IFW B43/ Tel: (01) 632-7239. e-mail: smilos@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 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 take this exam.

## Language

English (written, spoken, whatever)

## Course material

 Lectures Transparencies(1-in-1 version) Transparencies(4-in-1 version) Problems Misc. Lecture 1October 20(Basics I) [PDF][PS] [PDF][PS] [PDF][PS] [PDF][PS] (Oct 20) (Oct 20) (Oct 20) (Oct 20) Lecture 2October 27(Basics II) [PDF][PS] [PDF][PS] [PDF][PS] (Oct 27) (Oct 27) (Oct 27) Lecture 3November 3(Extremal problems) [PDF][PS] [PDF][PS] [PDF][PS] (Nov 3) (Nov 3) (Nov 3) Lecture 4November 10(Trees) [PDF][PS] [PDF][PS] [PDF][PS] (Nov 10) (Nov 10) (Nov 10) Lecture 5November 17(Matchings I) [PDF][PS] [PDF][PS] [PDF][PS] (Nov 17) (Nov 17) (Nov 17) Lecture 6November 24(Matchings II) [PDF][PS] [PDF][PS] [PDF][PS] (Nov 24) (Nov 24) (Nov 24) Lecture 7December 1(Matchings III, Connectivity I) [PDF][PS] [PDF][PS] [PDF][PS] (Dec 1) (Dec 1) (Dec 1) Lecture 8December 8(Network Flows, Connectivity II) [PDF][PS] [PDF][PS] [PDF][PS] (Dec 8, rev) (Dec 8, rev) (Dec 8) Lecture 9December 15(Connectivity III, Coloring I) [PDF][PS] [PDF][PS] [PDF][PS] (revised Dec 22) (revised Dec 22) (Dec 15) Lecture 10December 22(Coloring II) [PDF][PS] No new transparencies No new transparencies (Dec 22) Lecture 11January 12(Edge-coloring) [PDF][PS] [PDF][PS] [PDF][PS] (Jan 12) (Jan 12) (Jan 12) Lecture 12January 19(Turán-Type Problems) [PDF][PS] [PDF][PS] [PDF][PS ] (Jan 19) (Jan 19) (Jan 19) Lecture 13January 26(Planar graphs I) [PDF][PS] [PDF][PS] [PDF][PS ] (Jan 26) (Jan 26) (Jan 26) Lecture 14February 2(Planar graphs II) No new transparencies No new transparencies [PDF][PS ] (Feb 2)