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Pebble motion problems occur in domains such as multi-robot motion planning (in which the pebbles are robots) and network routing (in which the pebbles are packets of data). The best-known example of a pebble motion problem is the famous 15 puzzle where a disordered group of fifteen tiles must be rearranged within a 4x4 grid by sliding one tile ...
Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling moves. A pebbling move on a graph consists of choosing a vertex with at least two pebbles, removing two pebbles from it, and adding one to an adjacent vertex (the second removed pebble is discarded from play). π(G), the pebbling number of a ...
The twelve pentominoes. After an introductory chapter that enumerates the polyominoes up to the hexominoes (made from six squares), the next two chapters of the book concern the pentominoes (made from five squares), the rectangular shapes that can be formed from them, and the subsets of an chessboard into which the twelve pentominoes can be packed.
An edge coloring with k colors is called a k-edge-coloring and is equivalent to the problem of partitioning the edge set into k matchings. The smallest number of colors needed for an edge coloring of a graph G is the chromatic index, or edge chromatic number, χ ′ (G). A Tait coloring is a 3-edge coloring of a cubic graph.
The goal remains to place a black pebble on the target vertex, but the pebbling of adjacent vertices may be done with pebbles of either color. Takumi Kasai et al. developed a game in which a pebble may be moved along an edge-arrow to an unoccupied vertex only if a second pebble is located at a third, control vertex; the goal is to move a pebble ...
In a traditional graph coloring, each vertex in a graph is assigned some color, and adjacent vertices — those connected by edges — must be assigned different colors. In a fractional coloring however, a set of colors is assigned to each vertex of a graph. The requirement about adjacent vertices still holds, so if two vertices are joined by ...
Opalescence or play of color is an optical phenomenon associated with the mineraloid gemstone opal, [1] a hydrated silicon dioxide. [2] This effect appears as a milky, translucent glow that changes with the angle of light, often creating a soft, pearly sheen that can display various colors or hues.
The Fechner color effect is an illusion of color seen when looking at certain rapidly changing or moving black-and-white patterns. They are also called pattern induced flicker colors (PIFCs). A sample of a Benham's top (animated version) The effect is most commonly demonstrated with a device known as Benham's top (also called Benham's disk ...