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# coloring

A *coloring* of a set $X$ by $Y$ is just a function $f:X\rightarrow Y$. 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 partition of $X$: for each $y\in Y$, $f^{{-1}}(y)$, 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 function, their union is $X$.

Related:

Partition, GraphTheory

Synonym:

colouring

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05D10*no label found*

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