On conditional edge-connectivity of graphs (Q1594865)

Let \(G\) be a graph. Then the conditional \(h\)-edge connectivity of \(G\), \(\lambda ^{(h)}(G),\) is the minimum cardinality \(\left|S\right|\) of a set \(S\) of edges of \(G\) so that \(G-S\) is disconnected and the minimum degree of \(G-S\) is at least \(h.\) It is shown in the paper that \(\lambda ^{(2)}(G)\) exists for \(k\)-regular graphs, \(k\geq 3\) and \(\lambda ^{(h)}(G)\leq g(k-2),\) where \(g\) is the girth of \(G.\)