In every sufficiently large structure which has been partitioned there will always be some
well-behaved structure in one of the parts. This takes many forms. For example, colorings of …

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

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 …

Ramsey theory is a fascinating topic. The author shares his view of the topic in this
contemporary overview of Ramsey theory. He presents from several points of view, adding …

We consider the coloring of certain distance graphs on the Euclidean plane. Namely, we ask
for the minimal number of colors needed to color all points of the plane in such a way that …

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 …

The study of combinatorial properties of finite point configurations is a vast area of research
in geometry, whose origins go back at least to the ancient Greeks. Since it includes virtually …

arXiv:2203.03006v1 [math.CO] 6 Mar 2022 Large cycles in generalized Johnson graphs Page
1 arXiv:2203.03006v1 [math.CO] 6 Mar 2022 Large cycles in generalized Johnson graphs …

The Axiom of Choice was used implicitly throughout the XIX century. A careful observation
would uncover that it was used for proving even such a classic result as the sequential …