Non removable edges in 3-connected cubic graphs (Q1175559)

Graph \(G\) is cyclically \(k\)-edge-connected if the minimum number of edges whose removal leaves at least two components each containing a cycle is at least \(k\). This paper investigates the structure of the subgraph induced by the non-\(k\)-removable edges in a cyclically \(k\)-edge-connected cubic graph, where edge \(xy\) of \(G\) is ``\(k\)-removable'' if \(G-x-y\) remains cyclically \(k\)-edge-connected.