In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter 2. For a tournament T of diameter 2, we show 2 ≤ − →rc(T ) ≤ 3. Furthermore, we provide a general upper bound on the rainbow k-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of kth diameter 2 has rainbow k-co...

We prove several results regarding rainbow cycles within edge-colored complete graphs. We refute a conjecture by Ball, Pultr, and Vojtěchovský [BPV05] by showing that if such a coloring does not contain a rainbow n-cycle, where n is odd, then it also does not contain rainbow cycles of all sufficiently large lengths. In addition, we present two examples which demonstrate that this result does no...

The Debye series is developed for electromagnetic scattering by a spheroid in order to decompose the far-zone fields into various physical processes. The geometrical rainbow angle and supernumerary spacing parameter are determined from the Debye intensity by fitting the results to an Airy function and comparing them to their assumed values in ray optics and Airy theory, respectively. Eccentrici...

We report what is believed to be the first photographic recording of a quaternary rainbow in nature. It appears on the Sun side of the sky with its red arc at a radius of about 45° from the Sun. The original pictures have been subjected to various forms of image processing to reveal the tertiary rainbow as well as the quaternary rainbow, which are separated by only a few degrees with their colo...

A 3–coloring of the elements of an abelian group is said to be rainbow–free if there is no 3–term arithmetic progression with its members having pairwise distinct colors. We give a structural characterization of rainbow–free colorings of abelian groups. This characterization proves a conjecture of Jungić et al. on the size of the smallest chromatic class of a rainbow–free 3–coloring of cyclic g...

The direct predatory effects of introduced rainbow trout Oncorhynchus mykiss on native longnose dace Rhinichthys cataractae were examined using a series of in-stream enclosures to determine if presence, density, or acclimation period of rainbow trout influenced survival of longnose dace. The number of longnose dace remaining in enclosures over the first 72 hours after rainbow trout introduction...

A path in an edge-colored graph G, where adjacent edges may be colored the same, is called a rainbow path if no two edges of the path are colored the same. For a κ-connected graph G and an integer k with 1 ≤ k ≤ κ, the rainbow k-connectivity rck(G) of G is defined as the minimum integer j for which there exists a j-edge-coloring of G such that every two distinct vertices of G are connected by k...

An Evaluation of Stress Induced Hortality of Stocked Catchable-sized Rainbow Trout in Temple Fork of the Logan River

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