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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 ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 16 February 2025. For other color lists, see Lists of colors. This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "List of colors" alphabetical ...
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 ...
Pebble grey: RAL 7033: Cement grey: RAL 7034: Yellow grey: RAL 7035: Light grey: ICE train text, electrical and instrumentation panels. RAL 7036: Platinum grey: RAL 7037: Dusty grey: RAL 7038: Agate grey: RAL 7039: Quartz grey: RAL 7040: Window grey: RAL 7042: Traffic grey A: RAL 7043: Traffic grey B: RAL 7044: Silk grey: RAL 7045: Telegrey 1: ...
The sheen [4] or gloss level of a paint is principally determined by the ratio of resinous, adhesive binder, which solidifies after drying, and solid, powdery pigment.The more binder the coating contains, the more regular reflection will be made from its smooth surface; conversely, with less binder, grains of pigment become exposed to the surface, scattering the light and providing matte ...
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.
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
According to Jensen & Toft (1995), the problem was first formulated by Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) had earlier published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961).