Related papers: Robert Grosseteste's colours
A proper $q$-coloring of a graph is an assignment of one of $q$ colors to each vertex of the graph so that adjacent vertices are colored differently. Sample uniformly among all proper $q$-colorings of a large discrete cube in the integer…
A hypergraph is 2-intersecting if any two edges intersect in at least two vertices. Blais, Weinstein and Yoshida asked (as a first step to a more general problem) whether every 2-intersecting hypergraph has a vertex coloring with a constant…
Physical colors, i.e. reflected or emitted lights entering the eyes from a visual environment, are converted into perceived colors sensed by humans by neurophysiological mechanisms. These processes involve both three types of…
The research documents the impact of a teaching experiment designed in order to make students consider not only the spectral composition of light but also its intensity when they interpret colour phenomena. The analysis of eight recorded…
Given an edge colouring of a graph with a set of $m$ colours, we say that the graph is (exactly) $m$-coloured if each of the colours is used. We consider edge colourings of the complete graph on $\mathbb{N}$ with infinitely many colours and…
We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We also show that the closely related problem of…
Colour symmetries with ten colours are presented for different tilings. In many cases, the existence of these colourings were predicted by group theoretical methods. Only in a few cases explicit constructions were known, sometimes using…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
In his recent work, Andrews revisited two-color partitions with certain restrictions on the differences between consecutive parts, and he established three theorems linking these two-color partitions with more familiar kinds of partitions.…
The paper proves the existence of monochrome standard simplexes of a given volume on a multidimensional rational lattice painted in a finite number of colors.
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
In this work, an attempt is presented to understand the contribution of Galileo Galilei in the field of the History of Ideas, from the moment he points a spyglass to the sky. For that, it was previously necessary that Giotto painting the…
We consider the enumeration of plane trees (rooted ordered trees) whose vertices are colored according to a specific coloring rule that prescribes which possible pairs of colors can occur as the colors of a parent vertex and its child. This…
Barnette identified two interesting classes of cubic polyhedral graphs for which he conjectured the existence of a Hamiltonian cycle. Goodey proved the conjecture for the intersection of the two classes. We examine these classes from the…
We suggest a new color distance based on two observations. First, perceptual color differences were designed to be used to compare very similar colors. They do not capture human perception for medium and large color differences well.…
De Broglie's original idea that a photon is composed of a neutrino-antineutrino pair bound by some interaction was severely modified by Jordan. Although Jordan addressed an important problem (photon statistics) that de Broglie had not…
In the paper we prove, in particular, that for any measurable coloring of the euclidian plane into two colours there is a monochromatic triangle with some restrictions on the sides. Also we consider similar problems in finite fields…
We study two models of the Majority problem. We are given n balls and an unknown coloring of them with two colors. We can ask sets of balls of size k as queries, and in the so-called General Model the answer to a query shows if all the…
We discuss three rainbow theories created by Descartes, Newton and Young. The note is written primary for school students.
The approach is through a singularity analysis of generating functions for 3- and 4-connected triangulations, asymptotic analysis, properties of the ${{}_3F_2}$ hypergeometric series, and Tutte's enumerative work on planar maps and…