图的着色及应用

图的着色(Graph Coloring)

按照某种规则对一个图的每个顶点或者边分配一个颜色(编号)，称为对图的着色。能按此规则完成着色的最小颜色数称为色数(chromatic number)，记为χ(G)。

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. –wikipedia

几种常用的图着色及应用

顶点着色(Vertex Coloring, also known as Proper Coloring)

任意一个结点，它的邻居的结点颜色不能和它一样。也就是说，同一条边的两个结点颜色不一样。顶点着色是图着色的基础。点着色要求图不能有自环，就是不能存在两个端点一样的边。但是图可以是多重图。