Restricted edge connectivity of regular graphs (Q2778142)

An edge cut which separates a connected graph into parts with order at least 2 is called restricted edge cut. A graph \(G\) is called maximal restricted edge connected if the restricted edge connectivity number (the cardinality of a minimum restricted edge cut) of \(G\) equals the minimum edge degree; see \textit{A.-H. Esfahanian} and \textit{S. L. Hakimi} [Inf. Process. Lett. 27, 195-199 (1988; Zbl 0633.05045)]. Here the author proves that every \(k\)-regular graph with \(k\geq 2\) and \(|G|\geq 4\) is maximal restricted edge connected if \(2k>|G|\).