$4.(2$ points$)$ Find the minimal $\backslash ($ k $\backslash )$ for which the graph below has a correct $\backslash ($ k $\backslash )-$coloring. $($A correct $\backslash ($ k $\backslash )$ coloring is a coloring of vertices in $\backslash ($ k $\backslash )$ colors, such that ends of each edge have different colors.$)$ Provide a correct $\backslash ($ k $\backslash )-$coloring and explain why $\backslash (($k$-1)\backslash )$ colors are not sufficient. $($The coloring may be provided as a mapping, like $"1-$ red, $2-$ blue, $3-$ green, $4-$ red, $...")$