Look at the graph G G below, in which two (unknown to us) graphs G 1 G 1 ​ and G 2 G 2 ​ are connected by some "crossover gadget'' of four vertices. Which of the following statements are true for all such G G, i.e., regardless of G 1 , G 2 G 1 ​ ,G 2 ​ ? 1 point G G has a Hamiltonian cycle if and only if G 1 G 1 ​ and G 2 G 2 ​ have a Hamiltonian path. If G G has a Hamiltonian cycle then it has a Hamiltonian path both endpoints of which belong to the central four vertices. The number of different Hamiltonian cycles of G G is even. The number of Hamiltonian paths in G G is odd. The number of Hamiltonian paths in G G is even.