Extremal problems in hypergraph colouring originate implicitly from Hilbert's theorem on
monochromatic affine cubes (1892) and van der Waerden's theorem on monochromatic …

Начнем с базовых определений. Пара множеств H:=(V, E) называется гиперграфом,
если V конечно, а E⊂ 2V. При этом V называется множеством вершин, а E …

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 …

The paper deals with panchromatic 3-colorings of random hypergraphs. A vertex 3-coloring
is said to be panchromatic for a hypergraph if every color can be found on every edge. Let H …

Basics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students
interested in becoming familiar with a dynamic segment of contemporary mathematics that …

We investigate several functions related to the r-color off-diagonal van der Waerden
numbers w (m 1,…, mr), where w (m 1,…, mr) is the minimal integer n such that every r …

The paper deals with an extremal problem concerning equitable colorings of uniform
hypergraph. Recall that a vertex coloring of a hypergraph H is called proper if there are no …

In this paper we prove a new recurrence relation on the van der Waerden numbers, w (r, k).
In particular, if p is a prime and p≤ k then w (r, k)> p⋅ wr− rp, k− 1. This recurrence gives the …

The paper deals with an extremal problem concerning colorings of hypergraphs with
bounded edge degrees. Consider the family of b-simple hypergraphs, in which any two …

The paper deals with an extremal problem concerning colorings of hypergraphs with
bounded edge degrees. Consider the family of b-simple hypergraphs, in which any two …