On the 3-restricted edge connectivity of permutation graphs

Abstract: An edge cut of a connected graph is a -restricted edge cut if is disconnected, and every component of has at least vertices. The -restricted edge connectivity is defined as the minimum cardinality over all -restricted edge cuts. A permutation graph is obtained by taking two disjoint copies of a graph and adding a perfect matching between the two copies. The -restricted edge connectivity of a permutation graph is upper bounded by the so-called minimum -edge degree. In this paper some sufficient conditions guaranteeing optimal -restricted edge connectivity and super -restricted edge connectivity for permutation graphs are presented for . [Copyright &y& Elsevier]