Bounded-endvertex path-packing conjecture for degenerate graphs

Let $k$ be a positive integer, let $G$ be a graph of degeneracy $d$, and let $c_k$ denote a constant depending on $k$. A collection of paths is edge-disjoint if no two paths share an edge, and it is maximal if no further path of the specified length can be added while preserving edge-disjointness. Bounded-endvertex path-packing conjecture. There is a maximal collection $\mathcal{C}$ of edge-disjoint paths of length $2k$ in $G$ such that every vertex of $G$ is an endvertex of at most $c_kd$ paths in $\mathcal{C}$. This is presented as an open question motivated by a proposition in the paper.