The Pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is True

Abstract

We prove that for any positive integers $k$ and $d$, if a graph $G$ has maximum average degree at most $2k+\frac{2d}{d+k+1}$, then $G$ decomposes into $k+1$ pseudoforests $C_1,\dots ,C_{k+1}$ such that there is an $i$ such that for every connected component $C$ of $C_i$, we have that $e(C)\le d$.

14 pages, 3 figures. arXiv admin note: text overlap with arXiv:1904.12435