On a series of problems related to the Borsuk and Nelson-Erdős-Hadwiger problems.

In the present paper, a series of problems connecting the Borsuk and Nelson-Erdős-Hadwiger classical problems in combinatorial geometry is considered. The problem has to do with finding the number χ( n, a, d) equal to the minimal number of colors needed to color an arbitrary set of diameter d in n-dimensional Euclidean space in such a way that the distance between points of the same color cannot be equal to a. Some new lower bounds for the quantity χ( n, a, d) are obtained. [ABSTRACT FROM AUTHOR]