7 problems

Bang-Jensen–Yeo conjecture. There exists an integer $K$ such that every $K$-arc-strong digraph has a strong arc decomposition.

Bang-Jensen and Yeo's conjecture. There exists an integer $K$ such that every $K$-arc-strong digraph has a strong arc decomposition.

Let $\mathcal H_2$ be the smallest class of digraphs containing symmetric odd cycles and closed under taking directed Hajós joins and $2$-Hajós tree joins. A digraph is $2$-extrema…

Arc-avoidance conjecture. The digraph $D\setminus A'$ is supereulerian.

Bang–Jensen–Thomassé's conjecture. Every digraph $D$ with $\lambda(D)\geq\alpha(D)$ is supereulerian.

Bang-Jensen and Yeo's conjecture. For every $\lambda\ge 2$ there is a finite set ${\cal S}_{\lambda}$ of digraphs such that every $\lambda$-arc-strong semicomplete digraph $D$ cont…

Special-case conjecture. There exists a natural number $k$ such that every digraph $D$ which is both $k$-arc-strong and $k$-arc-antistrong has arc-disjoint strong spanning subdigra…