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.

Open problems of Erdos

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 5th.

Near perfect coverings in graphs and hypergraphs

On p-intersection representations

Theta p of complete balanced r-partite graph

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