Let be $n_1$, $n_2$ such natural numbers that $n_1\geq 3$ and $n_2\geq 3$ and let be $G_{n1,n2}$ a graph that takes shape by taking $G_{n_1}$, the cycle of $n_1$ vertices, and $G_{n_2}$ the cycle of $n_2$ vertices, and linking all of $G_{n_1}$ vertices with all of $G_{n_2}$ vertices.
a) For which values of $n_1,n_2$ has the graph $G_{n1,n2}$ an Euler cycle ?
b) For which values of ${n_1,n_2}$ has the graph $G_{n1,n2}$ a Hamilton cycle ?
c) For which values of ${n_1,n_2}$ is the graph $G_{n1,n2}$ a 5-colorable but not 4-colorable?
Indication: Show first that in each legal(valid) coloration of $G_{n1,n2}$ the sets of colours that are used for $G_{n_1}$ vertices and $G_{n_2}$ vertices they have to to be foreign from each other.