Related papers: A Ramsey Class for Steiner Systems
For positive integers $n,r,s$ with $r > s$, the set-coloring Ramsey number $R(n;r,s)$ is the minimum $N$ such that if every edge of the complete graph $K_N$ receives a set of $s$ colors from a palette of $r$ colors, then there is guaranteed…
An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic substructure. The locally graphic behaviors are formalized in…
Several methods for generating random Steiner triple systems (STSs) have been proposed in the literature, such as Stinson's hill-climbing algorithm and Cameron's algorithm, but these are not yet completely understood. Those algorithms, as…
In the parlance of relational structures, the Finite Ramsey Theorem states that the class of all finite chains has the Ramsey property. A classical result of J. Ne\v{s}et\v{r}il and V. R\"{o}dl claims that the class of all finite posets…
Ramsey theory enables re-shaping of the basic ideas of quantum mechanics. Quantum observables represented by linear Hermitian operators are seen as the vertices of a graph. Relations of commutation define the coloring of edges linking the…
An ordered graph is a graph equipped with a linear ordering of its vertex set. A pair of ordered graphs is Ramsey finite if it has only finitely many minimal ordered Ramsey graphs and Ramsey infinite otherwise. Here an ordered graph F is an…
Many important problems in combinatorics and other related areas can be phrased in the language of independent sets in hypergraphs. Recently Balogh, Morris and Samotij, and independently Saxton and Thomason developed very general container…
We apply the Ramsey theory to the analysis of geometrical properties of closed contours. Consider a set of six points placed on a closed contour. The straight lines connecting these points are y_ik (x)={\alpha}_ik x+\b{eta}_ik (i,k=1...6),…
The class of finite distributive lattices, as many other classes of structures, does not have the Ramsey property. It is quite common, though, that after expanding the structures with appropriately chosen linear orders the resulting class…
We characterize a class of topological Ramsey spaces such that each element $\mathcal R$ of the class induces a collection $\{\mathcal R_k\}_{k<\omega}$ of projected spaces which have the property that every Baire set is Ramsey. Every…
A novel form of Ramsey narrowing is identified and characterized. For long-lived coherent atomic states coupled by laser fields, the diffusion of atoms in-and-out of the laser beam induces a spectral narrowing of the atomic resonance…
An online Ramsey game is a game between Builder and Painter, alternating in turns. They are given a graph $H$ and a graph $G$ of an infinite set of independent vertices. In each round Builder draws an edge and Painter colors it either red…
In this paper we study Tur\'an and Ramsey numbers in linear triple systems, defined as $3$-uniform hypergraphs in which any two triples intersect in at most one vertex. A famous result of Ruzsa and Szemer\'edi is that for any fixed $c>0$…
We prove that for any choice of parameters $k,t,\lambda$ the class of all finite ordered designs with parameters $k,t,\lambda$ is a Ramsey class.
Concept induction requires the extraction and naming of concepts from noisy perceptual experience. For supervised approaches, as the number of concepts grows, so does the number of required training examples. Philosophers, psychologists,…
In randomly created structures (be they natural or artificial) very often there exist ordered substructures. In this Hungarian language scientific essay we will present some of such structures in graph theory. E.g. R\'edei's theorem, Ramsey…
Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded linear rankwidth are MSO-transductions of paths -- a result that shows a strong link between the properties of these graph classes considered from the…
In Euclidean Ramsey Theory usually we are looking for monochromatic configurations in the Euclidean space, whose points are colored with a fixed number of colors. In the canonical version, the number of colors is arbitrary, and we are…
In recent years, there has been much progress in the field of structural Ramsey theory, in particular in the study of big Ramsey degrees. In all known examples of infinite structures with finite big Ramsey degrees, there is in fact a single…
We consider a generalisation of the classical Ramsey theory setting to a setting where each of the edges of the underlying host graph is coloured with a {\em set} of colours (instead of just one colour). We give bounds for monochromatic…