Supereulerian Oriented Graphs With Large Arc‐Strong Connectivity

ABSTRACT An oriented graph is a digraph whose underlying graph is simple. Bang‐Jensen and Thomassé conjectured that every digraph with arc‐strong connectivity at least as large as its independence number must be supereulerian. We introduce max–min ditrails in a digraph and investigate the relationship between the arc‐strong connectivity and matching number to assure the supereulericity of an oriented graph . Utilizing the max–min ditrails with the related counting arguments, it is proved that every oriented graph with is supereulerian. This bound is the best possible.