Exercise 21, § 5

Let K be the graph associated with the quiver whose set of vertices is $\{1,2,3\} \times \{0,1\}$, whose set of arrows is the set of pairs of the form $((a,0),(b,1))$, for $a, b\in \{1,2,3\}$, and whose source and target mappings are respectively deduced from the first and second projection (“Kuratowski graph”). Prove that the graph K is not planar.