Consider a line segment R consisting of n facilities. Each facility is a point on R and it needs to be assigned exactly one of the colors from a given palette of c colors. At an instant of time only the facilities of one particular color are ‘active’ and all other facilities are ‘dormant’. For the set of facilities of a particular color, we compute the one dimensional Voronoi diagram, and find ...

We study dynamic conflict-free colorings in the plane, where the goal is to maintain a conflict-free coloring (CF-coloring for short) under insertions and deletions. First we consider CF-colorings of a set S of unit squares with respect to points. Our method maintains a CF-coloring that uses O(logn) colors at any time, where n is the current number of squares in S, at the cost of only O(logn) r...

For a fixed graph $H$, what is the smallest number of colors $C$ such that there proper edge-coloring complete $K_n$ with containing no two vertex-disjoint color-isomor...

Consider the coloring of a vertex-labelled r-uniform hypergraph G(V,E), where V is the vertex set of n labelled vertices, and E is the set of hyperedges. In case of proper bicoloring, given two colors, we need to assign each vertex with one of the colors so that none of the hyperedges is monochromatic. This may not always be possible. In such cases, we use multiple bicolorings to ensure that ea...

Watermarking of printed materials has usually focused on process inks of cyan, magenta, yellow and black (CMYK). In packaging, almost three out of four printed materials include spot colors. Spot colors are special premixed inks, which can be produced in a vibrant range of colors, often outside the CMYK color gamut. In embedding a watermark into printed material, a common approach is to modify ...

In this paper we study the problem of coloring graphs in an online manner. The only known deterministic online graph coloring algorithm with a sublinear performance function was found by Lov&z, Saks and Trotter [5]. Their algorithm colors graphs of c h r s matic number x with no more than ((2xn)/log*n) colors, where n is the number of vertices. They point out that the performance can be improve...

In 2001, Brualdi and Hollingsworth proved that an edge-colored balanced complete bipartite graph Kn,n with a color set C = {1, 2, 3, . . . , 2n − 1} has a heterochromatic spanning tree if the number of edges colored with colors in R is more than |R|/4 for any non-empty subset R ⊆ C, where a heterochromatic spanning tree is a spanning tree whose edges have distinct colors, namely, any color appe...

Objective(s):There is much evidence indicating that depression is influenced by the levels of neurotransmitters such as dopamine, GABA and adrenaline. The current study we designed to investigate the effect of exposure of pregnant rats to different colors on neurotransmitters level, as indicators of mood disorders in off springs. Materials and Methods:Five groups of pregnant female Wistar rats ...