Rainbow trout are classified as Oncorhynchus mykiss, and as such belong to the same genus as Pacific salmon, and to the family Salmonidae, which includes Atlantic salmon (Salmo salar), various trout (Salvelinus sp.), Arctic char (Salvelinus alpinus), Arctic grayling (Thymallus arcticus) and whitefish (Coregonus sp.). Rainbow trout are native to areas around the North Pacific Ocean, from souther...

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 makeG rainbowconnected. In this paper we show some new bounds for the rainbow connection number of graphs depending on the minimum degree and...

An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we show that rc(G) ≤ 3 if |E(G)| ≥ ( n−2 2 ) + 2, and rc(G) ≤ 4 if |E(G)| ≥ ( n−3 2 ) + 3. These bounds...

Given a function f a subset of its domain is a rainbow subset for f if f is one to one on it. We start with an old Erdős Problem: Assume f is a coloring of the pairs of ω1 with three colors such that every subset A of ω1 of size ω1 contains a pair of each color. Does there exist a rainbow triangle ? We investigate rainbow problems and results of this style for colorings of pairs establishing ne...

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 binomial random graphs at the connectivity threshold p = log n+ω ...

The rainbow trapping effect has been demonstrated in electromagnetic and acoustic waves. In this study, rainbow trapping of ultrasonic guided waves is achieved in chirped phononic crystal plates that spatially modulate the dispersion, group velocity, and stopband. The rainbow trapping is related to the progressively slowing group velocity, and the extremely low group velocity near the lower bou...