Trail-Connected Digraphs with Given Local Structures

Abstract

For a digraph [Formula: see text], if [Formula: see text] contains a spanning closed trail, then [Formula: see text] is supereulerian. If for any pairs vertices [Formula: see text] and [Formula: see text] of [Formula: see text], [Formula: see text] contains both a spanning [Formula: see text]-trail and a spanning [Formula: see text]-trail, then [Formula: see text] is strongly trail-connected. If [Formula: see text] is a strongly trail-connected digraph, then [Formula: see text] is a supereulerian digraph. Algefari et al. proved that every symmetrically connected digraph and every partially symmetric digraph are supereulerian. In this paper, we prove that every symmetrically connected digraph and every partially symmetric digraph are strongly trail-connected digraphs.