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Exact coloring of the complete graph K 6. Every n-vertex complete graph K n has an exact coloring with n colors, obtained by giving each vertex a distinct color. Every graph with an n-color exact coloring may be obtained as a detachment of a complete graph, a graph obtained from the complete graph by splitting each vertex into an independent set and reconnecting each edge incident to the ...
The vertex coloring game was introduced in 1981 by Steven Brams as a map-coloring game [1] [2] and rediscovered ten years after by Bodlaender. [3] Its rules are as follows: Alice and Bob color the vertices of a graph G with a set k of colors. Alice and Bob take turns, coloring properly an uncolored vertex (in the standard version, Alice begins).
Similarly, an edge coloring assigns a color to each edges so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face (or region) so that no two faces that share a boundary have the same color. Vertex coloring is often used to introduce graph coloring problems, since other coloring ...
Back vertex distance BVP: Back vertex power CD: Centration distance C/D: Cup–disc ratio CF: Count fingers vision – state distance c/o or c.o. Complains of CT: Cover test c/u: Check up CW: Close work Δ: Prism dioptre D: Dioptres DC: Dioptres cylinder DNA: Did not attend DOB: Date of birth DS: Dioptres sphere DV: Distance vision DVD ...
A parsimonious coloring, for a given graph and vertex ordering, has been defined to be a coloring produced by a greedy algorithm that colors the vertices in the given order, and only introduces a new color when all previous colors are adjacent to the given vertex, but can choose which color to use (instead of always choosing the smallest) when ...
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.
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An eye chart is a chart used to measure visual acuity comprising lines of optotypes in ranges of sizes. Optotypes are the letters or symbols shown on an eye chart. [ 1 ] Eye charts are often used by health care professionals, such as optometrists , physicians and nurses , to screen persons for vision impairment .