The arboricity of a graph is the minimal number of trees which cover the entire graph. It is equal to the minimal number of forests that partition the graph. A 2-sphere is a finite simple graph for which every unit sphere is a cyclic graph with 4 or more elements (aka a connected 1-sphere, a graph which has the property that every unit sphere is a 0-sphere). The Three Tree Theorem tells that the arboricity of a 2-sphere is 3. In the talk we give a proof of the lower and upper bound. The construction part will be written down in more detail. I had tried for a while to prove the arboricity=3 result without the 4 color theorem. Now, I know that the arboricity = 3 result is actually equivalent to the 4 color theorem.
