Supereulerian bipartite digraphs

A digraph D is supereulerian if D has a spanning closed ditrail. Bang‐Jensen and Thomassé conjectured that if the arc‐strong connectivity λ ( D ) of a digraph D is not less than the independence number α ( D ) , then D is supereulerian. A digraph is bipartite if its underlying graph is bipartite. Letα ′ ( D )be the size of a maximum matching of D . We prove that if D is a bipartite digraph satisfying λ ( D ) ≥ ⌊α ′ ( D ) 2 ⌋ + 1 , then D is supereulerian. Consequently, every bipartite digraph D satisfying λ ( D ) ≥ ⌊ α ( D ) 2 ⌋ + 1 is supereulerian. The bound of our main result is best possible.