chromatic number

chromatic number

[krō′mad·ik ′nəm·bər]
(mathematics)
For a specified surface, the smallest number n such that for any decomposition of the surface into regions the regions can be colored with n colors in such a way that no two adjacent regions have the same color.

chromatic number

(mathematics)
The smallest number of colours necessary to colour the nodes of a graph so that no two adjacent nodes have the same colour.

See also: four colour map theorem.

Graph Theory Lessons.

Eric Weisstein's World Of Mathematics.

The Geometry Center.
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References in periodicals archive ?
For the lower bound, let n = [chi](N) be the chromatic number of N, so that N [right arrow] [K.
The total chromatic number of G, denoted by [CHI]T(G), is the least k for which G has a k-total-coloring.
The total chromatic number of G, denoted by xt(G), is the least k for which G has a k-total-coloring.
We first state a purely topological result and then turn the existence of the vector bundle guaranteed by it into the existence of a graph with lower chromatic number than expected.
For example, minimally coloring an arrangement while avoiding monochromatic cells can be reformulated as finding the chromatic number of the hypergraph [H.
The minimal value of k is called the chromatic number of the graph G, commonly denoted by X(G).
Kostochka, List edge chromatic number of graphs with large girth, Discrete Math.
The acyclic edge chromatic number (also called acyclic chromatic index), denoted by a'(G), is the minimum number of colors required to acyclically edge color G.
5] decreases/increases the split- chromatic number exactly by one?
The chromatic number [chi](G) is the least integer k for which there is a k-coloring of G: The chromatic number can be formulated in terms of homomorphisms.
The strong oriented chromatic number of an oriented graph is the minimal order of a group M such that G has an M-strong-oriented coloring.
Then, we provide a formula based on 0-1 integer programming to get chromatic number in 9-CAA.