Bang–Jensen–Thomassé's arc-connectivity conjecture for supereulerian digraphs

Let $D$ be a digraph. Write $\lambda(D)$ for its arc-connectivity and $\alpha(D)$ for its independence number. A digraph is supereulerian if it has a spanning eulerian subdigraph.

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

This conjecture generalizes Camion's theorem and is open even for digraphs of independence number $2$, although it has been verified for several classes of digraphs.