Add to ORKGIs it true that for any coloring of the points of R in two colors there is an ε >0 such that one of the color classes contains pairs of points at every distance smaller than ε ? We show that the answer to this question is no
AbstractThe problem of colouring the real line so that the distance between like coloured numbers do...
Suppose D is a subset of all positive integers Z. The distance graph G(Z; D) is the graph with verte...
Abstract. Given a graph G = (V, E), a (d, k)-coloring is a function from the vertices V to colors {1...
AbstractLet S be a metric space and let k be a positive integer. Define χ̂(k)(S) to be the smallest ...
AbstractWe develop a method of estimating the (upper) density of a set in Rn or Sn for which the dis...
Given a natural $n$, we construct a two-coloring of $\mathbb{R}^n$ with the maximum metric satisfyin...
summary:What is the least number of colours which can be used to colour all points of the real Eucli...
AbstractLet G be an r-chromatic graph with an s-colorable subgraph, each of whose components is s-co...
AbstractFix positive integers k′, d′, k, d such that k′/d′>k/d⩾2. If P is a set of vertices in a (k,...
htmlabstractIn this paper we derive new upper bounds for the densities of measurable sets in R^n whi...
AbstractSuppose the graph G can be r-colored using colors 1,2,…,r, so that no vertex is adjacent to ...
AbstractWe consider the following problem: given suitable integers χ and p, what is the smallest val...
Fix a real number 0. Let = {1 } if 6 = 1; otherwise = {1} may simply be written as 1. A sub...
We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd ...
International audienceFor an integer q ⩾ 2 and an even integer d, consider the graph obtained from a...
AbstractThe problem of colouring the real line so that the distance between like coloured numbers do...
Suppose D is a subset of all positive integers Z. The distance graph G(Z; D) is the graph with verte...
Abstract. Given a graph G = (V, E), a (d, k)-coloring is a function from the vertices V to colors {1...
AbstractLet S be a metric space and let k be a positive integer. Define χ̂(k)(S) to be the smallest ...
AbstractWe develop a method of estimating the (upper) density of a set in Rn or Sn for which the dis...
Given a natural $n$, we construct a two-coloring of $\mathbb{R}^n$ with the maximum metric satisfyin...
summary:What is the least number of colours which can be used to colour all points of the real Eucli...
AbstractLet G be an r-chromatic graph with an s-colorable subgraph, each of whose components is s-co...
AbstractFix positive integers k′, d′, k, d such that k′/d′>k/d⩾2. If P is a set of vertices in a (k,...
htmlabstractIn this paper we derive new upper bounds for the densities of measurable sets in R^n whi...
AbstractSuppose the graph G can be r-colored using colors 1,2,…,r, so that no vertex is adjacent to ...
AbstractWe consider the following problem: given suitable integers χ and p, what is the smallest val...
Fix a real number 0. Let = {1 } if 6 = 1; otherwise = {1} may simply be written as 1. A sub...
We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd ...
International audienceFor an integer q ⩾ 2 and an even integer d, consider the graph obtained from a...
AbstractThe problem of colouring the real line so that the distance between like coloured numbers do...
Suppose D is a subset of all positive integers Z. The distance graph G(Z; D) is the graph with verte...
Abstract. Given a graph G = (V, E), a (d, k)-coloring is a function from the vertices V to colors {1...