A coloringMathworldPlanetmath of a set X by Y is just a functionMathworldPlanetmath f:XY. The term coloring is used because the function can be thought of as assigning a “color” from Y to each element of X.

Any coloring provides a partitionMathworldPlanetmathPlanetmath of X: for each yY, f-1(y), the set of elements x such that f(x)=y, is one element of the partition. Since f is a function, the sets in the partition are disjoint, and since it is a total functionMathworldPlanetmath, their union is X.

Title coloring
Canonical name Coloring
Date of creation 2013-03-22 12:55:43
Last modified on 2013-03-22 12:55:43
Owner Henry (455)
Last modified by Henry (455)
Numerical id 5
Author Henry (455)
Entry type Definition
Classification msc 05D10
Synonym colouring
Related topic Partition
Related topic GraphTheory