Theorem 2 (Kuratowski) says that a graph is nonplanar if and only if it contains a subgraph homeomorphic to $ K_{3,3} $ or $ K_{5} $.
Looking at the given graph, it is obvious to see that it contains a subgraph homeomorphic to $ K_{5} $ (a, c, d, f, and h form the pentagon, and everything inside of the pentagon forms the rest of $ K_{5} $. Therefore, the given graph is nonplanar.
--Aoser 16:59, 5 December 2008 (UTC)
