Complex sentence: In a maximal planar graph, the book thickness is two if and only if a Hamiltonian cycle exists; therefore, it is also NP-complete to test whether the book thickness of a given maximal planar graph is two.
Split into simpler sentences: In a maximal planar graph, the book thickness is two if and only if a Hamiltonian cycle exists. Therefore, it is also NP-complete to test whether the book thickness of a given maximal planar graph is two.