We present a stacked and contrast-enhanced image comprised of 12 digital photographs that shows a series of color hues in the correct order and location to be part of the seventh-order rainbow. The observation was made on September 22, 2013, near Magdalena in New Mexico (USA). The seventh-order rainbow is located at 64° from the Sun in a region of the sky with little interference from the zero-...

A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster. The rainbow vertex-connection of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. In this paper, we study the computational...

An edge colored graph G is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this work we study the rainbow connectivity of the binomial graph G = G(n, p) at the connectivity threshold p = ...

For a graph G, let f : V (G) → P({1, 2, . . . , k}) be a function. If for each vertex v ∈ V (G) such that f(v) = ∅ we have ∪u∈N(v)f(u) = {1, 2, . . . , k}, then f is called a k-rainbow dominating function (or simply kRDF) of G. The weight, w(f), of a kRDF f is defined as w(f) = ∑ v∈V (G) |f(v)|. The minimum weight of a kRDF of G is called the k-rainbow domination number of G, and is denoted by ...

An edge-coloured path is rainbow if the colours of its edges are distinct. For a positive integer k, an edge-colouring of a graph G is rainbow k-connected if any two vertices of G are connected by k internally vertex-disjoint rainbow paths. The rainbow k-connection number rck(G) is defined to be the minimum integer t such that there exists an edge-colouring of G with t colours which is rainbow ...

An edge-coloured path is rainbow if all of its edges have distinct colours. For a connected graph G, the rainbow connection number rc(G) of G is the minimum number of colours in an edge-colouring of G such that, any two vertices are connected by a rainbow path. Similarly, the strong rainbow connection number src(G) ofG is the minimum number of colours in an edge-colouring of G such that, any tw...

BACKGROUND Estimates of fishing and natural mortality are important for understanding, and ultimately managing, commercial and recreational fisheries. High reward tags with fixed station acoustic telemetry provides a promising approach to monitoring mortality rates in large lake recreational fisheries. Kootenay Lake is a large lake which supports an important recreational fishery for large Bull...

An H-factor of a graph G is a spanning subgraph of G whose connected components are isomorphic to H. Given a properly edge-colored graph G, a rainbow H-subgraph of G is an H-subgraph of G whose edges have distinct colors. A rainbow H-factor is an H-factor whose components are rainbow H-subgraphs. The following result is proved. If H is any fixed graph with h vertices then every properly edge-co...

Multiple Hemoglobin Components in Cutthroat and Rainbow Trout Multiple hemoglobin components in fish is a well-documented phenomenon, with cutthroat trout having twelve (Figure 1a) and rainbow trout having nine (Figure 1b) hemoglobin components (Braman et al.1977). A high-resolution starch gel electrophoresis method was developed to resolve eight negatively charged hemoglobin components from bo...

Let G = (V (G), E(G)) be a nontrivial connected graph of order n with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ N, where adjacent edges may be colored the same. A tree T in G is a rainbow tree if no two edges of T receive the same color. For a vertex set S ⊆ V (G), a tree connecting S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such t...