Graph coloring

A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible.

This graph can be 3-colored in 12 different ways.

All non-isomorphic graphs on 3 vertices and their chromatic polynomials. The empty graph E3 (red) admits a 1-coloring, the others admit no such colorings. The green graph admits 12 colorings with 3 colors.

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.

单词	Face coloring
释义	Face coloring 英语百科 Graph coloring In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.
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Face coloring

Graph coloring