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Sum coloring of a tree. The sum of the labels is 11, smaller than could be achieved using only two labels. In graph theory, a sum coloring of a graph is a labeling of its vertices by positive integers, with no two adjacent vertices having equal labels, that minimizes the sum of the labels. The minimum sum that can be achieved is called the ...
Number bonds are often learned in sets for which the sum is a common round number such as 10 or 20. Having acquired some familiar number bonds, children should also soon learn how to use them to develop strategies to complete more complicated sums, for example by navigating from a new sum to an adjacent number bond they know, i.e. 5 + 2 and 4 ...
The empty graph E 3 (red) admits a 1-coloring; the complete graph K 3 (blue) admits a 3-coloring; the other graphs admit a 2-coloring. Main article: Chromatic polynomial The chromatic polynomial counts the number of ways a graph can be colored using some of a given number of colors.
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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A color in the RGB color model is described by indicating how much of each of the red, green, and blue is included. The color is expressed as an RGB triplet (r,g,b), each component of which can vary from zero to a defined maximum value. If all the components are at zero the result is black; if all are at maximum, the result is the brightest ...
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In graph-theoretic terms, the theorem states that for loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.