Related papers: Descartes-Newton-Young rainbow
Given an edge-colored graph $G$, we denote the number of colors as $c(G)$, and the number of edges as $e(G)$. An edge-colored graph is rainbow if no two edges share the same color. A proper $mK_3$ is a vertex disjoint union of $m$ rainbow…
These notes are connected to a "potpourri" topics class and deal with some special cases of norms of various objects which arise in classical analysis.
We study the rainbow version of the graph commonness property: a graph $H$ is $r$-rainbow common if the number of rainbow copies of $H$ (where all edges have distinct colors) in an $r$-coloring of edges of $K_n$ is maximized asymptotically…
We prove two results regarding cycles in properly edge-colored graphs. First, we make a small improvement to the recent breakthrough work of Alon, Pokrovskiy and Sudakov who showed that every properly edge-colored complete graph $G$ on $n$…
It is shown as experiments and theories about the nature of light led to the special theory of relativity. The most important facts for the emergence of the theory proposed by Einstein in 1905 are presented.
For a connected graph $G$, the \emph{rainbow connection number $rc(G)$} of a graph $G$ was introduced by Chartrand et al. In "Chakraborty et al., Hardness and algorithms for rainbow connection, J. Combin. Optim. 21(2011), 330--347",…
In this note we shall give a new proof to a quadrature formulae due to Newton.
What do we mean by neutrino astronomy? Which information is it able to provide us and which is its potential? To address these questions, we discuss three among the most relevant sources of neutrinos: the Sun; the core collapse supernovae;…
The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.
We study the structured rainbow Ramsey theory at uncountable cardinals. When compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not only is of a certain cardinality but also satisfies certain…
This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD),…
The present note sketches a theory of constructs.
In offered work short historical excursus to the classical theory of light is presented: Grimaldi, Fermat, Newton, Huygens, Young, Fresnel, Fraunhofer, and Gauss. The ray analog of wave model of light and Huygens-Fresnel's elementary waves…
For a fixed graph $F$, the rainbow Tur\'an number $\mathrm{ex^*}(n,F)$ is the largest number of edges possible in an $n$-vertex graph which admits a rainbow-$F$-free proper edge-coloring. We focus on the rainbow Tur\'an numbers of trees…
A famous conjecture of Caccetta and H\"aggkvist is that in a digraph on $n$ vertices and minimum out-degree at least $\frac{n}{r}$ there is a directed cycle of length $r$ or less. We consider the following generalization: in an undirected…
Beginning with a decomposition of the Newtonian field of gravity, I show that four classical color fields can be associated with the gravitational field. The meaning of color here is that these fields do not add up to yield the Newtonian…
In most studies related to colouring of graphs and perhaps in the study of other invariants and variants of graphs, the restrictions of non-triviality and connectedness are placed upon graphs. For the introduction to comp\^{o}nent\u{a}…
Based on a new theory of causality [1] and its development to the theory of the Universe [2], we show, in this paper, new ideas for building a theory of everything.
Let p be a prime number and Zp be the cyclic group of order p. A coloring of Zp is called rainbow-free with respect to a certain equation, if it contains no rainbow solution of the same, that is, a solution whose elements have pairwise…
The solar neutrino problem, atmospheric neutrino problem, and the existence of hot dark matter can all be economically accounted for using only the three known neutrinos if these neutrinos all have nearly degenerate masses of a few eV. We…