### Sunday, July 12

## MS4

Recent Developments on the Regularity Lemma

3:30 PM-6:00 PM

*Room: Sidney Smith 2110*

Szemeredi's Regularity Lemma is one of the most powerful tools in graph theory. It states that every graph can be approximated by random graphs. It has important applications in various areas of mathematics and computer science. Recently there have been several interesting new developments -- Komlos, Sarkozy and Szemeredi developed the Blow-up Lemma and used it together with the Regularity Lemma to attack several long-standing open problems in extremal graph theory. Eaton and Rodl proved a variation of the Regularity Lemma and used it to obtain improved Ramsey numbers for certain classes of graphs. Haxell used another variant of the Regularity Lemma to prove a result about partitioning complete bipartite graphs into monochromatic cycles.

**Organizer: Gábor N. Sárközy**

*Worcester Polytechnic Institute*

**3:30 The Regularity Lemma and the Blow-up Lemma**
- Gábor N. Sárközy, Organizer
**4:00 Ramsey Numbers for Sparse Graphs**
- Nancy Eaton, University of Rhode Island
**4:30 Packing and Covering Triangles in Dense Graphs**
- Penny Haxell, University of Waterloo, Canada
**5:00 Regularity Lemma and Its Applications in Combinatorics**
- Miklos Simonovits, Hungarian Academy of Sciences, Hungary
**5:30 Title to be announced**
- Vera T. Sós, Hungarian Academy of Sciences, Hungary

*MMD, 6/29/98*