Related papers: Rainbow Thresholds
We review the status of inclusive |Vub| measurements where many new results have become available recently.
In this paper, we prove a conjecture of Aharoni and Howard on the existence of rainbow (transversal) matchings in sufficiently large families $\mathcal F_1,\ldots, \mathcal F_s$ of tuples in $\{1,\ldots, n\}^k$, provided $s\ge 470.$
Given a graph $G=(V,E)$ on $n$ vertices and an assignment of colours to its edges, a set of edges $S \subseteq E$ is said to be rainbow if edges from $S$ have pairwise different colours assigned to them. In this paper, we investigate…
A rainbow colouring of a connected graph is a colouring of the edges of the graph, such that every pair of vertices is connected by at least one path in which no two edges are coloured the same. Such a colouring using minimum possible…
The differential scattering cross section for charged relativistic particles moving parallel close to the crystalline plane of atoms was obtained. The rainbow scattering effect in the approximation of continuous potential was demonstrated.…
Given a family $\mathcal G$ of graphs on a common vertex set $X$, we say that $\mathcal G$ is rainbow connected if for every vertex pair $u,v \in X$, there exists a path from $u$ to $v$ that uses at most one edge from each graph in…
We discuss the expected minimum cost of rainbow spanning trees and Hamilton cycles in randomly edge colored random graphs.
We experimentally achieve wave mode conversion and rainbow trapping in an elastic waveguide loaded with an array of resonators. Rainbow trapping is a phenomenon that induces wave confinement as a result of a spatial variation of the wave…
Given a graph $G$ and a coloring of its edges, a subgraph of $G$ is called rainbow if its edges have distinct colors. The rainbow girth of an edge coloring of G is the minimum length of a rainbow cycle in G. A generalization of the famous…
We report on the experimental demonstration of the broadband "trapped rainbow" in the visible range using arrays of adiabatically tapered optical nano waveguides. Being a distinct case of the slow light phenomenon, the trapped rainbow…
We prove a rainbow version of the blow-up lemma of Koml\'os, S\'ark\"ozy and Szemer\'edi for $\mu n$-bounded edge colourings. This enables the systematic study of rainbow embeddings of bounded degree spanning subgraphs. As one application,…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
This appendix for our article, "Almost-rainbow edge-colorings of some small subgraphs", contains the full proof of Theorem 4.1.
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
A conjecture by Aharoni and Berger states that every family of $n$ matchings of size $n+1$ in a bipartite multigraph contains a rainbow matching of size $n$. In this paper we prove that matching sizes of $(3/2 + o(1)) n$ suffice to…
A subgraph of an edge-coloured graph is called rainbow if all its edges have different colours. We prove a rainbow version of the blow-up lemma of Koml\'os, S\'ark\"ozy and Szemer\'edi that applies to almost optimally bounded colourings. A…
A rainbow is a captivating natural phenomenon resulting from the refraction, dispersion, and reflection of sunlight within water droplets. Traditional classroom demonstrations often focus on qualitative explanations of the formation of…
As a testament to their success, the theory of random forests has long been outpaced by their application in practice. In this paper, we take a step towards narrowing this gap by providing a consistency result for online random forests.
The threshold estimate derived in previous versions of this paper was incorrect; this note explains the flaw. A new proof is discussed in arXiv:0809.5063.
A new theory of edge waves over a slowly varying depth.