Lower bound for feedback vertex sets in digraphs of bounded degeneracy

Let $k$ be the degeneracy of a digraph, let $n$ be a positive integer, and write $f$ for the size of a minimum feedback vertex set.

The paper conjectures that there is an $\varepsilon>0$ such that for every $n$ there exists an $n$-vertex digraph of degeneracy $k$ whose minimum feedback vertex set has size

$$f\geq \frac{k-(2-\varepsilon)\log_2(k+1)}{k+1}n.$$

The paper obtains upper bounds for digraphs of bounded treewidth and degeneracy, but does not construct lower bounds that significantly improve the probabilistic tournament bounds of Erdős and Moser; this conjecture proposes such an improved lower-bound construction.