An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. Krivelevich and Yuster have shown that a connected graph G with n vertices has rc(G) < 20n δ(G) [M. Krivelevich and...

Abstract: A 2-rainbow domination function of a graph G = (V, E) is a function f mapping each vertex v to a subset of {1, 2} such that ⋃ u∈N(v) f (u) = {1, 2} when f (v) = �, where N(v) is the open neighborhood of v. The weight of f is denoted by wf (G) = ∑ v∈V �f (v)�. The 2-rainbow domination number, denoted by r2(G), is the smallest wf (G) among all 2-rainbow domination functions f of G. The ...

The innate immune system of fish is critical for rapid detection and immediate response to infection, as well as to orchestrate the adaptive branch of the immune system. Rainbow trout Oncorhynchus mykiss ladderlectin and intelectin are plasma pattern recognition receptors (PRR) for bacterial and fungal pathogens of rainbow trout, but their role as PRRs for virus is unknown. Viral hemorrhagic se...

A connected edge-colored graph G is rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors; the rainbow connection number rc(G) of G is the minimum number of colors such that G is rainbow-connected. We consider families F of connected graphs for which there is a constant kF such that, for every connected F-free graph G, rc(G) ≤ diam...

Rainbow is a fast asymmetric multivariate signature algorithm proposed by J. Ding and D. Schmidt in [5]. This paper presents a cryptanalysis of Rainbow which enables an attacker provided with the public key to recover an equivalent representation of the secret key, thus allowing her to efficiently forge a signature of any message. For the set of parameter values recommended by the authors of Ra...

We study the consistency of the ladder approximation and the rainbow approximation of the Dyson-Schwinger equation of QCD. By considering the non-Abelian property of QCD, we show that the QED-type Ward-Takahashi identity is not required for the rainbow-ladder approximation of QCD. It indicates that there does not exists any internal inconsistency in the usual rainbow-ladder approximation of QCD...

In a graph G with a given edge colouring, a rainbow path is a path all of whose edges have distinct colours. The minimum number of colours required to colour the edges of G so that every pair of vertices is joined by at least one rainbow path is called the rainbow connection number rc(G) of the graph G. For any graph G, rc(G) > diam(G). We will show that for the Erdős–Rényi random graph G(n, p)...

PURPOSE To report and document a case of successful rainbow glare correction using undersurface ablation of the LASIK flap. METHODS A 33-year-old woman was treated bilaterally for myopia using femtosecond laser-assisted LASIK with the FS200 femtosecond laser (Alcon Laboratories, Inc., Fort Worth, TX). Postoperatively, she complained of rainbow glare in her right eye, and presented some residu...

In this paper we consider properly edge-colored graphs, i.e. two edges with the same color cannot share an endpoint, so each color class is a matching. A matching is called rainbow if its edges have different colors. The minimum degree of a graph is denoted by δ(G). We show that properly edge colored graphs G with |V (G)| ≥ 4δ(G) − 3 have rainbow matchings of size δ(G), this gives the best know...

Physiological and biochemical factors affecting carotenoid utilization in salmonid fish. Gregory Ian Page Carotenoid utilization in rainbow trout (Oncorhynchus mykiss Walbaum) and Atlantic salmon (Salmo sa/ar L.) has been investigated with respect to tissue distribution of carotenoids and the role of the liver on the bioavailability of the lipid soluble carotenoids, astaxanthin and canthaxanthi...