## Arboricity of Surfaces

We aim to write down a short proof of the statement that a planar graph has arboricity 3 or less.

We aim to write down a short proof of the statement that a planar graph has arboricity 3 or less.

We explain why the arboricity of 3 spheres can take values between 4 and 7 and mention that for 3 manifolds the upper bound is 9 (but believed to be 7).

We look at the problem to find the possible arboricities which a 3-sphere can have.

We work on the result that any 2-sphere can be covered by 3 trees.

In other words: three trees suffice.

The three tree theorem tells that any discrete 2-sphere has arboricity exctly 3.

We aim to show that the Lusternik-Schnirelmann category of a graph is bound by the augmented dimension. We can try to prove this by using tree coverings and so look at arboricity.