The two sets formula_1 and formula_2 may be thought of as a coloring of the graph with two colors: if one colors all nodes in formula_1 blue, and all nodes in formula_2 green, each edge has endpoints of differing colors, as is required in the graph coloring problem. 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.