Spanning Trails that Join Given Edges in \(3\)-Edge-Connected Graphs

For given edges \(e_1, e_2 \in E(G)\), a spanning trail of \(G\) with \(e_1\) as the first edge and \(e_2\) as the last edge is called a spanning \((e_1, e_2)\)-trail. In this note, we consider best possible degree conditions to assure the existence of these trails for every pair of edges in a \(3\)-edge-connected graph \(G\).