In this lecture we use coupling to design a Markov chain to generate a uniform random proper coloring of a graph with q colors. Recall that a coloring of vertices of G with q colors is proper if any two adjacent vertices have distinct colors. Let G be a graph with maximum degree ∆. Obviously, any such graph has a coloring with q = ∆ + 1 colors: Greedily color every vertex with a color with is n...

this article is an attempt to investigate the aesthetics of color themes in arabic poetry. as a means of psychological description, color is one of the manifestations of realism in poetic images. in the application of colors some mythical and civilized structures are portrayed in the culture of nations. since languages have their own specific organizations of colors, the author aims to measure ...

the manifest of value of colors in nazik al-malaika s poemsali piranishal *khadije hashemi**from the early times, colors have played an important role in developing poeticimages, and colorful images are the realistic and sensory aspects among poets. poetshave used colorful words to explore and explain the relationship between poeticimages and sometimes they have used colorful words to express t...

A coloring of a graph G is an assignment of colors to the vertices of G such that any two vertices receive distinct colors whenever they are adjacent. An acyclic coloring of G is a coloring such that no cycle of G receives exactly two colors, and the acyclic chromatic number χA(G) of a graph G is the minimum number of colors in any such coloring of G. Given a graph G and an integer k, determini...

We consider vertex colorings of graphs in which adjacent vertices have distinct colors. A graph is s-chromatic if it is colorable in s colors and any coloring of it uses at least s colors. The forcing chromatic number Fχ(G) of an s-chromatic graph G is the smallest number of vertices which must be colored so that, with the restriction that s colors are used, every remaining vertex has its color...

We present several tools for use in approximation algorithms to color 3-chromatic graphs. We then use these techniques in an algorithm that colors any 3chromatic graph with O(n) colors (or more precisely O(n log n) colors) which improves the previous best bound of O(n) colors. We also illustrate these techniques by considering a problem in which the 3-chromatic graph is created not by a worst-c...

OBJECTIVES 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 ...

In this brief note, we give two partition statistics which explain the following partition congruences: b(5n + 4) ≡ 0 (mod 5), b(7n + a) ≡ 0 (mod 7), if a = 2, 3, 4, or 6. Here, b(n) is the number of 4-color partitions of n with colors r, y, o, and b subject to the restriction that the colors o and b appear only in even parts.