The Petersen graph is nonplanar. Any nonplanar graph has as minors either the complete graph formula_1, or the complete bipartite graph formula_5, but the Petersen graph has both as minors. The formula_1 minor can be formed by contracting the edges of a perfect matching, for instance the five short edges in the first picture. The formula_5 minor can be formed by deleting one vertex (for instance the central vertex of the 3-symmetric drawing) and contracting an edge incident to each neighbor of the deleted vertex.