# coloring

A *coloring ^{}* of a set $X$ by $Y$ is just a function

^{}$f:X\to Y$. 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 $X$.

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 |