Graph theory question about planar graphs

How can i prove that every planar graph can be expressed as a union of five edge-disjoint forests ?

I think I should use theorem that says : ' Every planar graph contains vertex with degree 5 or less' and maybe continue similalry to five color theorem, but I am not sure.

Any hints are welcomed.

Thanks for help.

EDIT
I narrowed it to this :

We know that every planar graph contains vertex of degree <=5. If we pull of this vertex with its adjacent edges, we will get a smaller graph with maximum of 5 edges, which we can easily distribute into 5 forests(or color into 5 different colors for easier imagination). We just repeat the process until we color the whole graph. Now we need to prove that there won't be any cyrcles in forests(triangles(or bigger) with all edges of the same color). I think it should be done by contradiction. If we assume that there is a cyrcle in one of the forests, there should be something that contradicts the algorithm. (When I tried some examples on paper, I found out that there were cases where 2/3 of a triangle was the same color, but never a full cyrcle.)
If you could tell me how to finish this, I would be very grateful.

• can we assume it is finite? Commented Jan 12, 2015 at 0:52
• Yes, we can assume that. Commented Jan 12, 2015 at 0:56

• @Lemonicious If you're doing it by induction, what can you say about $G-v$? Commented Jan 13, 2015 at 1:08
• @Lemonicious You don't really want to say "If G can be expressed as a union of 5 edge-disjoint forests then G - v can too", although that's true: after all, what we're trying to show is that $G$ can be expressed as a union of 5 edge-disjoint forests. Your second statement is closer: if we're using induction, our induction hypothesis tells us that $G-v$ can be expressed as a union of 5 edge-disjoint forests. Now we just need to figure out what to do with the 5 edges incident to $v$. Seems like we should try to fit them into the existing forests somehow. Commented Jan 13, 2015 at 2:43