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Wed, Dec 08

|ZOOM: 837 6398 9129 (wincom)

# Dr. Emily Heath, Iowa State University

The Erdős-Gyárfás Problem on Generalized Ramsey Numbers

## Time & Location

Dec 08, 2021, 3:00 p.m. EST

ZOOM: 837 6398 9129 (wincom)

## About the event

**The Erdős-Gyárfás Problem on Generalized Ramsey Numbers
**
A *(p, q)*-coloring of a graph *G* is an edge-coloring of *G* (not necessarily proper) in which each *p*-clique contains edges of at least *q* distinct colors. We are interested in the function *f(n, p, q)*, first introduced by Erdős and Shelah, which is the minimum number of colors needed for a *(p, q)*-coloring of the complete graph on *n* vertices. In 1997, Erdős and Gyárfás initiated the systematic study of this function. Among other results, they gave upper and lower bounds on *f(n, p, p)* which are still the best known bounds for general *p* today. In this talk, I will give an overview of this problem and describe recent improvements on the probabilistic upper bound of Erdős and Gyárfás for several small cases of *p*. This is joint work with Alex Cameron.