Alternatively, it is possible to show that any bridgeless bipartite planar graph with vertices and edges has by combining the Euler formula (where is the number of faces of a planar embedding) with the observation that the number of faces is at most half the number of edges (the vertices around each face must alternate between houses and utilities, so each face has at least four edges, and each edge belongs to exactly two faces). In the utility graph, and , violating this inequality, so the utility graph cannot be planar.