Uniform cyclic edge connectivity in cubic graphs (Q1180413)

A cubic graph \(G\) is called cyclically \(k\)-edge connected, \(k\geq 3\), if \(G\) is 3-edge connected and there is no set \(E\) of \(k-1\) or fewer edges such that \(G-E\) has at least two connected components containing cycles. \textit{D. Barnette} [Discrete Math. 7, 199-208 (1974; Zbl 0273.05104)] proved that all cyclically 5-edge connected cubic planar graphs can be obtained from the dodecahedron by a sequence of operations, i.e. adding an edge. Here the authors showed that all cyclically 5-edge connected cubic graphs can be generated by a small set of uniformly cyclically 5- edge connected cubic graphs, graphs without removable edges.