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The two sets <math>U</math> and <math>V</math> may be thought of as a coloring of the graph with two colors: if one colors all nodes in <math>U</math> blue, and all nodes in <math>V</math> green, each edge has endpoints of differing colors, as is required in the graph coloring problem.<ref name="s12">{{citation  | year = 2012}}.</ref>  In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another green, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color.

The two sets <math>U</math> and <math>V</math> may be thought of as a coloring of the graph with two colors: if one colors all nodes in <math>U</math> blue, and all nodes in <math>V</math> green, each edge has endpoints of differing colors, as is required in the graph coloring problem.<ref name="s12">{{citation  | year = 2012}}.</ref>  In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another green, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color.

通常可以将集合''U''和集合''V''视为被着色的两个图集：如果其中一个所有顶点为蓝色，另外一类为绿色，那么每条连边的两端必须具有不同的颜色。这是二分图必须满足的条件。相反，在非二分图（例如三角形）的情况下，这种着色要求是不可能的：因为如果一个顶点为蓝色，另一个为绿色，那么其剩下的第三个顶点将需要同时连接这两个颜色，显然这是不成立的，因为它违背了初始要求：二分图中所有顶点必须分为两个不相交且独立的集合''U''和''V''。即第三个顶点必须为两个颜色当中的一个。

通常可以将集合''U''和集合''V''视为被着色的两个图集：如果其中一个所有顶点为蓝色，另外一类为绿色，那么每条连边的两端必须具有不同的颜色。这是二分图必须满足的条件。相反，在非二分图（例如三角形）的情况下，这种着色要求是不可能的：因为如果一个顶点为蓝色，另一个为绿色，那么其剩下的第三个顶点将需要同时连接这两个颜色，显然这是不成立的，因为它违背了初始要求：二分图中所有顶点必须分为两个不相交且独立的集合''U''和''V''。即第三个顶点必须与另外两个点中的任意一个颜色相同。