A graph G is strongly spanning trailable if for any \(e_1=u_1v_1, e_2=u_2v_2\in E(G)\) (possibly \(e_1=e_2\)), \(G(e_1, e_2)\), which is obtained from G by replacing \(e_1\) by a path \(u_1v_{e_1}v_1\) and by replacing \(e_2\) by a path \(u_2v_{e_2}v_2\), has a spanning \((v_{e_1}, v_{e_2})\)-trail. A graph G is Hamilton-connected if there is a spanning path between any two vertices of V(G). In this paper, we first show that every 2-connected 3-edge-connected graph with circumference at most 8 is strongly spanning trailable with an exception of order 8. As applications, we prove that every 3-connected \(\{K_{1, 3}, N_{1, 2, 4}\}\)-free graph is Hamilton-connected and every 3-connected \(\{K_{1, 3}, P_{10}\}\)-free graph is Hamilton-connected with a well-defined exception. The last two results extend the results in Hu and Zhang (Graphs Comb 32: 685–705, 2016) and Bian et al. (Graphs Comb 30: 1099–1122, 2014) respectively.

如果对于E（G）\中的任何\（e_1 = u_1v_1，e_2 = u_2v_2 \）（可能是\（e_1 = e_2 \）），\（G（e_1，e_2）\），则图G可以强跨度跟踪从获得ģ通过替换\（E_1 \）由路径\（u_1v_ {E_1} V_1 \）和通过替换\（E_2 \）由路径\（u_2v_ {E_2} V_2 \） ，具有跨越\（（ v_ {e_1}，v_ {e_2}）\）-跟踪。如果在V（G的任意两个顶点之间存在跨越路径，则图G是汉密尔顿连通的）。在本文中，我们首先显示，每个圆周最多8个2连通3边连通图都具有很强的跨越性，除了8阶之外。作为应用，我们证明了每个3连通\（\ {K_ { 1，3}，N_ {1，2，4} \} \） -自由图是汉密尔顿连接的，每3个连接的\（\ {K_ {1，3}，P_ {10} \} \） -自由图图是具有明确定义的异常的Hamilton连接。最后两个结果扩展了Hu和Zhang（Graphs Comb 32：685-705，2016）和Bian等人的结果。（图表梳30：1099–1122，2014）。