In this chapter, we discuss two classical problems lying on the edge of graph theory and
combinatorial geometry. The first problem is due to E. Nelson. It consists of coloring metric …

In this paper, we overview three closely related problems: Nelson–Hadwiger problem on
coloring spaces with forbidden monochromatics distances; Borsuk's problem on partitioning …

Abstract Let χ (S rn− 1)) be the minimum number of colours needed to colour the points of a
sphere S rn− 1 of radius r\geqslant 1 2 in ℝ n so that any two points at the distance 1 apart …

This paper is devoted to the study of the graph sequence G n=(V n, E n), where V n is the set
of all vectors v∈ R n with coordinates in {− 1, 0, 1} such that| v|= 3 and E n consists of all …

This note relates to bounds on the chromatic number χ(R^n) of the Euclidean space, which
is the minimum number of colors needed to color all the points in R^n so that any two points …

О ХРОМАТИЧЕСКИХ ЧИСЛАХ ПРОСТРАНСТВ МАЛОЙ РАЗМЕРНОСТИ КОРЗИНА
ПОИСК НАВИГАТОР СЕССИЯ КОНТАКТЫ ИНФОРМАЦИЯ О ПУБЛИКАЦИИ eLIBRARY …

On the chromatic number of an infinitesimal plane layer Page 1 Algebra i analiz St. Petersburg
Math. J. Tom 29 (2017), 5 Vol. 29 (2018), No. 5, Pages 761–775 https://doi.org/10.1090/spmj/1515 …

В работе рассмотрен частный класс оценок, связанных с проблемой Нелсона–Эрдеша–
Хадвигера. Для двух типов пространств, евклидовых и с метрикой ℓ1, мы …

A particular class of estimates related to the Nelson–Erdős–Hadwiger problem is studied.
For two types of spaces, Euclidean and spaces with metric ℓ 1, certain series of distance …

Graphs which are analogs of Kneser graphs are studied. The problem of determining the
chromatic numbers of these graphs is considered. It is shown that their structure is similar to …