Kuratowski (1930) proved that any nonplanar graph "contains" (in a sense we explain below) a copy of K_5 or K_3.3. K_5 is also called the complete graph on five vertices. It is one of an infinite family of graphs K_n, each of which contains an edge between any two of its n vertices. K_3.3 is one of an infinite family of graphs K_m, n, each of which has m + n vertices Another famous nonplanar graph is the Petersen graph shown in Figure 25.8. Show that the Peterson graph "contains" a subdivided K_3.3, thus giving a different proof that the Petersen graph is nonplanar. Kuratowski (1930) proved that any nonplanar graph "contains" (in a sense we explain below) a copy of K_5 or K_3.3. K_5 is also called the complete graph on five vertices. It is one of an infinite family of graphs K_n, each of which contains an edge between any two of its n vertices. K_3.3 is one of an infinite family of graphs K_m, n, each of which has m + n vertices Another famous nonplanar graph is the Petersen graph shown in Figure 25.8. Show that the Peterson graph "contains" a subdivided K_3.3, thus giving a different proof that the Petersen graph is nonplanar