Supereulerian Extended Digraphs

Abstract:

      A digraph $D$ is supereulerian if $D$ has a spanning eulerian subdigraph. Bang-Jensen and Thomass\'{e} conjectured that if the arc-strong connectivity $\lambda(D)$ of a digraph $D$ is not less than the independence number $\alpha(D)$, then $D$ is supereulerian. In this paper, we prove that if $D$ is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfying $\lambda(D)\geq \alpha(D)$, then $D$ is supereulerian.