AbstractIt is shown that every red–blue coloring of the plane, without two blue points distance 1 apart, must have a red translate of every three-point configuration. A seven-point configuration S and a red–blue coloring are exhibited, which avoids both distance one in blue and translates of S in red
AbstractIn this paper we investigate colorings of sets avoiding similarly colored subsets. If S is a...
Is it true that for any coloring of the points of R in two colors there is an ε >0 such that one ...
We prove that for any planar convex body C there is a positive integer m with the property that any ...
AbstractThere exists a 2-colouring of the plane with red and blue and a configuration K of eight poi...
There exists a 2-coloring of the plane with red and blue and a configuration K of eight points (a re...
summary:What is the least number of colours which can be used to colour all points of the real Eucli...
Let ℓ_m be a sequence of m points on a line with consecutive points of distance one. For every natur...
AbstractThe chromatic number of the plane is the smallest number of colors needed in order to paint ...
Is it possible to color R^2 with 2 colors in such a way that the vertices of any unit equilateral tr...
Euclidean Ramsey theory is examining konfigurations of points, for which there exists n such that fo...
In a colouring of Rd a pair (S, s0) with S ⊆ Rd and with s0 ∈ S is almost-monochromatic if S \ {s0} ...
The old problem of determining the chromatic number of the plane is revisited. The question of the c...
AbstractA six-coloring of the euclidean plane is constructed such that the distance 1 is not realize...
AbstractIn this note we shall prove a geometric Ramsey theorem. Let T be a triangle with angles 30, ...
AbstractA proof is given of the (known) result that, if real n-dimensional Euclidean space Rn is cov...
AbstractIn this paper we investigate colorings of sets avoiding similarly colored subsets. If S is a...
Is it true that for any coloring of the points of R in two colors there is an ε >0 such that one ...
We prove that for any planar convex body C there is a positive integer m with the property that any ...
AbstractThere exists a 2-colouring of the plane with red and blue and a configuration K of eight poi...
There exists a 2-coloring of the plane with red and blue and a configuration K of eight points (a re...
summary:What is the least number of colours which can be used to colour all points of the real Eucli...
Let ℓ_m be a sequence of m points on a line with consecutive points of distance one. For every natur...
AbstractThe chromatic number of the plane is the smallest number of colors needed in order to paint ...
Is it possible to color R^2 with 2 colors in such a way that the vertices of any unit equilateral tr...
Euclidean Ramsey theory is examining konfigurations of points, for which there exists n such that fo...
In a colouring of Rd a pair (S, s0) with S ⊆ Rd and with s0 ∈ S is almost-monochromatic if S \ {s0} ...
The old problem of determining the chromatic number of the plane is revisited. The question of the c...
AbstractA six-coloring of the euclidean plane is constructed such that the distance 1 is not realize...
AbstractIn this note we shall prove a geometric Ramsey theorem. Let T be a triangle with angles 30, ...
AbstractA proof is given of the (known) result that, if real n-dimensional Euclidean space Rn is cov...
AbstractIn this paper we investigate colorings of sets avoiding similarly colored subsets. If S is a...
Is it true that for any coloring of the points of R in two colors there is an ε >0 such that one ...
We prove that for any planar convex body C there is a positive integer m with the property that any ...
DOI
Add to ORKG