An edge-coloured graph G is said to be rainbow-connected if any two vertices are connected by a path whose edges have different colours. The rainbow connection number of a graph is the minimum number of colours needed to make the graph rainbow-connected. This graph parameter was introduced by G. Chartrand, G.L. Johns, K.A. McKeon and P. Zhang in 2008. Since, the topic drew much attention, and v...

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such ...

The rainbow trout (Oncorhynchus mykiss) is one of the most widely used fish species in aquaculture and physiological research. In the present paper, we report the first cloning, 3D (three-dimensional) modelling, pharmacological characterization and tissue distribution of two melanocortin (MC) receptors in rainbow trout. Phylogenetic analysis indicates that these receptors are orthologues of the...

We derive sufficient conditions for the existence of rainbow cycles of all lengths in edge colourings of complete graphs. We also consider rainbow colorings of a certain class of trees.

A tree T , in an edge-colored graph G, is called a rainbow tree if no two edges of T are assigned the same color. A k-rainbow coloring of G is an edge coloring of G having the property that for every set S of k vertices of G, there exists a rainbow tree T in G such that S ⊆ V (T ). The minimum number of colors needed in a k-rainbow coloring of G is the k-rainbow index of G, denoted by rxk(G). G...

Global Rainbow Thermometry is presented. It is a new technique for measuring average size and temperature of spray droplets. For data inversion, a global rainbow pattern is employed, which is formed by constructive interference of laser-light scattering spherical droplets. The non-spherical droplets and liquid ligaments provide a uniform background and thus do not influence the interference pat...

The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in k colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors. Our main result states that for any k ≥ 2, there is no algorithm for Rainbow k-Coloring running in time 2 3/2), unless ETH fails. Motivated by this negative result we consider two paramet...

An edge-colored graph G is said to be rainbow connected if between each pair of vertices there exists a path which uses each color at most once. The rainbow connection number, denoted by rc(G), is the minimum number of colors needed to make G rainbow connected. Along with its variants, which consider vertex colorings and/or so-called strong colorings, the rainbow connection number has been stud...

Pit-1 is a pituitary-specific transcription factor responsible for activating growth hormone (GH) and prolactin genes. Here, we describe the isolation of a rainbow trout cDNA clone that contains the entire Pit-1 coding region. The deduced amino acid sequence contains 358 residues, encoding a 39-kDa protein. Comparison of the protein sequences of the rainbow trout and rat Pit-1 shows that the 16...

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such ...