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 prove several non-trivial upper bounds for rc(G), as well as determine sufficient conditions that gua...

OBJECTIVE High rates of psychotic experiences among detained adolescents have been reported. However, the significance of psychotic experiences in detained juveniles is still poorly understood. The current study, therefore, (1) examines whether psychotic experiences could be explained by substance use and/or traumatic experiences, and (2) investigates this objective without taking into account ...

s Elgersburg 2011 Rainbow Cycles in Cube Graphs Jens-P. Bode (Technische Universität Braunschweig) Joint work with A. Kemnitz and S. Struckmann A graph G is called rainbow with respect to an edge coloring if no two edges of G have the same color. Given a host graph H and a guest graph G ⊆ H, an edge coloring of H is called G-anti-Ramsey if no subgraph of H isomorphic to G is rainbow. The anti-R...

A path in an edge-colored graph, where adjacent edges may be colored the same, is a rainbow path if no two edges of it are colored the same. A nontrivial connected graph G is rainbow connected if there is a rainbow path connecting any two vertices, and the rainbow connection number of G, denoted by rc(G), is the minimum number of colors that are needed in order to make G rainbow connected. Char...

Consider a coloring of {1, 2, . . . , n} in 3 colors, where n ≡ 0 (mod 3). If all the color classes have the same cardinality, then there is a 3-term arithmetic progression whose elements are colored in distinct colors. This rainbow variant of van der Waerden’s theorem proves the conjecture of the second author.

Background: Leukocytospermia is found in both fertile and infertile men with and without evidence of infections of the genital tract. However, despite extensive research done in this subject, the clinical implications of this condition remain unclear. Leukocytes are also commonly found in semen samples, and a level above 1×106/mL is considered pathologic according to WHO criteria. Non-steroidal...

The aim of this study was to examine the changes in muscle proteome of the rainbow trout fed dietary β-glucan. The experimental diets contained 0 (control), 0.1% and 0.2% β-1,3/1,6 yeast glucan. First, feeding larvae were fed to apparent satiation nine times per day with their respective diets over two months. The percentage of body weight gain and feed efficiency of fish fed 0.2% diet was sign...

In this short note, we study pairwise edge-disjoint rainbow spanning trees in properly edge-coloured complete graphs, where a graph is rainbow if its edges have distinct colours. Brualdi and Hollingsworth conjectured that every Kn properly edge-coloured by n−1 colours has n/2 edge-disjoint rainbow spanning trees. Kaneko, Kano and Suzuki later suggested this should hold for every properly edge-c...