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，给出了每个此类图到准4-连通部分、轮图或加厚$K_{3,m}$的唯一分解。该构造是显式的、规范的，并且具有以下应用：我们得到了一个新定理，将所有Cayley图刻画为本质4-连通图、圈图或至多四个顶点的完全图，并且提供了Tutte轮定理的自动化证明。