Math 581: Topics in Graph Theory
Graphs and Geometry
(a.k.a. Signed Graphs and their Friends)

Fall 2008
Spring-Summer 2009
Spring 2010

This course is an introduction to fundamental concepts of signed graph theory, generalizations, and related geometry, including a dash of matroids. There is no official book but there are lots of papers available (electronically, and I can give real reprints of several of them to those who like that sort of thing). A linked list will be posted later. I'll recommend a basic graph theory book when I can think of one that's most appropriate. (Diestel or Tutte will be satisfactory though not perfect.)

The course is not normally suitable for first-year graduate students. However, there are no specific prerequisites except the traditional ``mathematical maturity''—not even a course in graph or matroid theory, though it will be helpful. Basic graduate algebra is very helpful.

Course time and place:

SPRING 2010:

Tu 12:00 - 1:05 in LN-2205,
Th 1:15 - 2:40 or earlier in LN-2206.

Office hours:

I will be happy to see graduate students at any time, as far as possible (that means, not early in the morning and not when I'm rushing to prepare a class). We can make appointments, but they're not required.

The Seminar

All students are strongly encouraged, if not required, to attend the Combinatorics Seminar, usually on Tuesdays, 1:15 - 2:15. 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. Ask questions!

Lecture notes

I will have you write up the notes of the lectures (in LaTeX). I'll use them to prepare lecture notes.

Link to the note-taking schedule and preparation guide.

Your grade will be based partly on your note-taking and write-ups. It may be based partly on student presentations. I will also meet with each of you individually on a regular basis.

Here is the Tex-files page from which you can download the Latex files of all the lectures.

Outline of Topics

See the Outline page.


For the complete list see the Readings page. Here is the most basic list.


Signed Graphs:

Geometry of Signed Graphs:

Biased Graphs and Gain Graphs:

To my home page.