Question 9
Let $\Gamma$ be a connected graph on $r + g + b + 1$ vertices. The edges of $\Gamma$ bear three colours: red, green, and blue. It turns out that $\Gamma$ has a spanning tree with exactly $r$ red edges, a spanning tree with exactly $g$ green edges, and a spanning tree with exactly $b$ blue edges. Prove that $\Gamma$ has a spanning tree with exactly $r$ red edges, exactly $g$ green edges, and exactly $b$ blue edges.