5 problems

Let ${\rm fasd}(\Delta,g)$ denote the supremum, over the relevant weighted orgraphs of maximum degree at most $\Delta$ and directed girth at least $g$, of the normalized feedback a…

Hanauer et al.'s conjecture. If $\Delta\leq 5$, then

Hanauer's conjecture. If $\Delta\leq 5$, then

Let $G=(V,E)$ be a digraph on $n$ vertices, let $\beta(G)$ denote the minimum size of a feedback arc set, and let an $(r-1)$-free digraph be one containing no directed cycle of len…

Let $m\ge 3$, and let $G$ be an $m$-free digraph, meaning that $G$ has no directed cycle of length at most $m$. Let $\beta(G)$ be the minimum number of edges whose removal makes…