Spring 2008

MTH 692 – Topics in Advanced Graph
Theory

__Objectives:__
Explore topics in advanced graph theory including extremal graph theory, graph
Ramsey theory, and the random graph. Obtain, read, and present research
papers on these topics. In particular we will focus on papers of Paul
Erdös, 1913-1996.

__Assignments:__
From the list provided, obtain as many papers as you can. First see if
URI carries the Journal issues in hard copy or as an online subscription.
If not, request the article through interlibrary loan.

Select some to present, including the necessary background.
You don’t have to present the entire paper, but be sure to present some of the
proofs in enough detail that all can follow. Students take turns
throughout the semester.

Take two sessions of the Combinatorics Seminar to present one of
your papers. Background in one session, proofs in second session.

Final report. This is a collection in chronological order of
all of your presentations. You may collaborate. **Final Report**

Course material for weeks 1, 2, and 3.

The
representation of a graph by set intersections, a paper

Set representaions of graphs – presentation notes

p-intersection representations of the random graph

A Discrete Math
Day at Smith College, April 5^{th}.

Near perfect coverings in graphs and hypergraphs

On p-intersection representations

Theta p of complete balanced r-partite graph