# Coloring¶

Graph coloring is the problem of assigning a color to the vertices of a graph in a way that no adjacent vertices have the same color.

## Example¶

The map-coloring problem is to assign a color to each region of a map (represented by a vertex on a graph) such that any two regions sharing a border (represented by an edge of the graph) have different colors.

`is_vertex_coloring` (G, coloring) |
Determines whether the given coloring is a vertex coloring of graph G. |

`min_vertex_color` (G[, sampler, chromatic_lb, …]) |
Returns an approximate minimum vertex coloring. |

`min_vertex_color_qubo` (G[, chromatic_lb, …]) |
Return a QUBO with ground states corresponding to a minimum vertex coloring. |

`vertex_color` (G, colors[, sampler]) |
Returns an approximate vertex coloring. |

`vertex_color_qubo` (G, colors) |
Return the QUBO with ground states corresponding to a vertex coloring. |