We offer a new structural basis for the theory of 3-connected graphs, providing a unique decomposition of every such graph into parts that are either quasi 4-connected, wheels, or thickened $K_{3,m}$'s. Our construction is explicit, canonical, and has the following applications: we obtain a new theorem characterising all Cayley graphs as either essentially 4-connected, cycles, or complete graphs on at most four vertices, and we provide an automatic proof of Tutte's wheel theorem.

翻译：我们为3-连通图理论提供了新的结构基础，使得每个此类图都能唯一分解为准4连通图、轮图或加厚$K_{3,m}$图三类部分。该构造具有显式性与规范不变性，并具备以下应用：获得了刻画所有Cayley图的新定理——其要么本质上为4连通图、圈图，要么是顶点数不超过4的完全图；同时给出了Tutte轮定理的自动化证明。