COURSE
ANNOUNCEMENT
M690I, SPRING 2006:
Extremal
Graph Theory
INSTRUCTOR:
Prof. Ryan Martin
TIME:
12:40-2:00 TR
TOPICS:
Extremal graph theory is the study of how the intrinsic structure of
graphs ensures certain types of properties (e.g., cliques, colorings
and spanning subgraphs) under appropriate conditions (e.g., edge
density and minimum degree).
We shall discuss standard results, such as those due to
Turán, Ramsey, Dirac and Hajnal and Szemerédi, but
focus our attention on two ideas that have relatively recently
become powerful tools in this area of mathematics: the Regularity
lemma and the Blow-up lemma. These have been used, often in tandem,
to produce a variety of surprising and powerful results. The
Regularity lemma has proven quite versatile. It has applications
not only in graph theory, but also among other topics from
hypergraphs to number theory.
We will cover other topics, including the probabilistic method
and expander graphs as well as other topics, as time permits.
PREREQUISITES:
M607 OR M314, M/STAT
341, AND M317
OR M307.
| UPCOMING
TALK (GRADUATE
STUDENT
COLLOQUIUM): |
| TITLE: |
The Small World problem and so much more! 6666... degrees of graph theory. |
| 305 CARVER | |
4:10-5:00 | |
OCT 19 |
|
| UPCOMING
TALK (DISCRETE
MATH
SEMINAR): |
| TITLE: |
An application of the Regularity lemma. |
| 074 CARVER |
|
2:10-3:00 | |
OCT 25: Part I &
NOV 1: Part II |
