research results and facts of indigenous sheep production were reviewed with the aim of delivering relevant information for the beneficiaries. the common production system used in ethiopia was the extensive type, which was characterized by small flock sizes and the flock being periodically devastated by diseases. some indigenous sheep groups of the country were characterized and their names wer...

Research results and facts of indigenous sheep production were reviewed with the aim of delivering relevant information for the beneficiaries. The common production system used in Ethiopia was the extensive type, which was characterized by small flock sizes and the flock being periodically devastated by diseases. Some indigenous sheep groups of the country were characterized and their names wer...

The edge-face chromatic number Xe / (G) of a plane graph G is the smallest number of colors assigned to the edges and faces of G so that any two adjacent or incident elements have different colors. Borodin(1994) proved that L1( G) ~ Xe/ (G) :::; L1( G) + 1 for each plane graph G with ~(G) ~ 10 and the bounds are sharp. The main result of this paper is to give a sufficient and necessary conditio...

A subgraph of an edge-colored graph is called rainbow if all of its edges have different colors. For a graph G and a positive integer n, the anti-Ramsey number ar(n, G) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of H. Anti-Ramsey numbers were introduced by Erdős, Simonovits and Sós and studied in numerous papers. Let G be a graph with anti-Ramsey number ar(n,...

This Letter presents the color distributions of the globular cluster (GC) systems of 12 Virgo elliptical galaxies, measured using data from the Hubble Space Telescope. Bright galaxies with large numbers of detected GC’s show two distinct cluster populations with mean V − I colors near 1.01 and 1.26. The GC population of M86 is a clear exception; its color distribution shows a single sharp peak ...

We study the degenerate, the star and the degenerate star chromatic numbers and their relation to the genus of graphs. As a tool we prove the following strengthening of a result of Fertin et al. [8]: If G is a graph of maximum degree ∆, then G admits a degenerate star coloring using O(∆) colors. We use this result to prove that every graph of genus g admits a degenerate star coloring with O(g) ...

An edge-colored graph G, where adjacent edges may be colored the same, is rainbow connected if any two vertices of G are connected by a path whose edges have distinct colors. The rainbow connection number rc(G) of a connected graph G is the smallest number of colors that are needed in order to make G rainbow connected. In this paper, we give a sharp upper bound that rc(G) ≤ ⌈n2 ⌉ for any 2-conn...

This Letter presents the color distributions of the globular cluster (GC) systems of 12 Virgo elliptical galaxies, measured using data from the Hubble Space Telescope. Bright galaxies with large numbers of detected GC’s show two distinct cluster populations with mean V − I colors near 1.01 and 1.26. The GC population of M86 is a clear exception; its color distribution shows a single sharp peak ...

This paper is concerned with efficiently coloring sparse graphs in the distributed setting with as few colors as possible. According to the celebrated Four Color Theorem, planar graphs can be colored with at most 4 colors, and the proof gives a (sequential) quadratic algorithm finding such a coloring. A natural problem is to improve this complexity in the distributed setting. Using the fact tha...

A path in an edge-colored graph is called a rainbow path if the edges on it have distinct colors. For k ≥ 1, the rainbow-k-connectivity of a graph G, denoted rck(G), is the minimum number of colors required to color the edges of G in such a way that every two distinct vertices are connected by at least k internally vertex-disjoint rainbow paths. In this paper, we study rainbow-k-connectivity in...