Canonical Decompositions of 3-Connected Graphs
arXiv:2304.00945 · doi:10.19086/aic.2025.7 10.1109/FOCS57990.2023.00115
Abstract
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 's. Our construction is explicit, canonical, and has the following applications: we obtain a new theorem characterising all finite 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.
73 pages, 21 figures