Let $G= (V,E)$ be a graph such that:
$E = E_1 \cup E_2$
$G_1 = (V, E_1)$ is planar
$G_2 = (V, E_2)$ is forest
Proof that chromatic number is $< 9$
Each planar graph has chromatic number $\le 4$. Also each forest has chromatic number $2$ if $|V| > 1$
But how can I connect that and have convince about chromatic number $<9$?