NEW LOWER BOUNDS FOR THE CHROMATIC NUMBER OF A SPACE WITH FORBIDDEN ISOSCELES TRIANGLES

摘要

The work is devoted to the classical Nelson-Hadwiger problem in the combinatorial geometry (see [8, 22, 23, 32, 33]). In its most general form, this problem is formulated as follows: find the chromatic number of a set X subject to a set of forbidden configurations A is contained in 2~X, i.e., the number χ(X,A) = min{χ: X = X_1 ∪ • • • ∪ X_χ (A)i, (A)A ∈ A, A(is contained in)X_i}.