Let's assume that Graph $G = <V,E>$ has two Spanning Trees $G_a = <V, T_1>$ and $G_b = <V,T_2>$ where $T_1 \cap T_2 = \emptyset$ and $T_1 \cup T_2 = E$. Prove that $\chi(G) \le 4$
$\chi(G)$ is the chromatic number.
Well I know that every tree can be colored by only two colors. Will this help ?
I think it's necessary to disprove the existence of $K_5$ clique. But how ?