On a problem of P. Erdös
by
Andrei M. Raigorodskii
Moscow State University, Mechanics and Mathematics Faculty, Department of Mathematical Statistics and Random Processes

In our talk, the famous question going back to P. Erdös will be discussed: what is the minimum number of colors needed to paint all the points in a metric space so that the points at unit distance apart would receive different colors? Numerous combinatorial and number-theoretic results have been obtained in connection with the question. We shall present a historical overview of the subject and emphasize the most recent methods leading to the development of new trends in the research.

Date received: February 9, 2004