Math 581: Topics in Graph Theory
Introduction to Graph Theory
Spring 2003

This course is an introduction to fundamental concepts of graph theory. We study the book

W.T. Tutte,
Graph Theory,
Cambridge University Press.

To the extent there is a special emphasis, it is on the structure of graphs, in particular contributions of Tutte, arguably the greatest graph theorist of the last century. (A short biography from Tutte's home university. The New York Times obituary.)

The course is not normally suitable for first-year graduate students. However, there are no specific prerequisites except the traditional ``mathematical maturity''. Basic graduate algebra is very helpful.

Course time and place:

PLACE: LN-2205

Mon. and Fri. 2:20-3:20.
Wed. usually 2:20-3:20, but on some days (to be announced in advance if possible) 1:10-2:10.

Office hours:

My regular office hours, which are mainly for the undergraduates, are

M (usually, unless there's a seminar at 1:10): 1:20-2:00
W: 1:20-2:00, 4:45-5:30
Th (usually): 1:30-2:30
F: 1:20-2:00, 4:45-5:30
I will be happy to see you at these or other times as far as possible. If necessary we can make appointments.

The Seminar

All students are encouraged to attend the Combinatorics and Number Theory Seminar, usually on Mondays, 3:30 - 4:30. There will be talks you can't understand, as well as some you can't help understanding, on all kinds of topics in graph theory and other combinatorics as well as in number theory (and sometimes both at once). (You'll be surprised how much you learn by not understanding a great many talks.)

Course Procedure

I will lecture, for the most part.

Student work: You will have to work hard sometimes to understand the lectures and readings. Keep your colored pencils handy. I will find some way to give you a grade; I expect it will be based on a combination of handed-in problems and (later) student presentations. I will also (eventually!) meet with each of you individually on a regular basis.

I expect you to try all the exercises at the end of the chapters. You don't have to solve all of them! I will collect your written solutions to some or all of the following assignments, some from Tutte and some from the additional problems below. The list of hand-in problems is not compulsory but you should turn in as many as you can.

Syllabus and Assignments

The syllabus is tentative and partial. It will get filled out and corrected as the course progresses.

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