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The choosability (or list colorability or list chromatic number) ch(G) of a graph G is the least number k such that G is k-choosable. More generally, for a function f assigning a positive integer f ( v ) to each vertex v , a graph G is f -choosable (or f -list-colorable ) if it has a list coloring no matter how one assigns a list of f ( v ...
The smallest number of colors needed to color a graph G is called its chromatic number, and is often denoted χ(G). Sometimes γ(G) is used, since χ(G) is also used to denote the Euler characteristic of a graph. A graph that can be assigned a (proper) k-coloring is k-colorable, and it is k-chromatic if its chromatic number is exactly k.
The traditional color-coding algorithm is probabilistic, but it can be derandomized without much overhead in the running time. Color-coding also applies to the detection of cycles of a given length, and more generally it applies to the subgraph isomorphism problem (an NP-complete problem), where it yields polynomial time algorithms when the ...
Casual use in an engineering class has been cited as evidence of the sexism faced by women in scientific fields. [15] Latanya Arvette Sweeney , associate professor of computer science at Carnegie Mellon , mentions yet another as one reason why she felt alienated and eventually dropped out of MIT in the 1980s to form her own software company. [ 16 ]
The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most k different colors, for a given value of k, or with the fewest possible colors. The minimum required number of colors for the edges of a given graph is called the chromatic index of the graph. For example, the edges of the graph in the ...
Domain coloring plot of the function f(x) = (x 2 − 1)(x − 2 − i) 2 / x 2 + 2 + 2i , using the structured color function described below. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane. By assigning points on the ...
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