An Approximate Version of the Strong Nine Dragon Tree Conjecture

We prove the Strong Nine Dragon Tree Conjecture is true if we replace d with d + k/2 · (d/k+1 - 1) d/k+1. More precisely: let G be a graph and let d and k be positive integers. If γ(G) ≤ k + d/d + k + 1, then there is a partition into $k + 1$ forests, where in one forest every connected component has at most d + k/2 · (d/k+1 - 1) d/k+1 edges.