Abstract
An edge cut W of a connected graph G is a k -restricted edge cut if G − W is disconnected, and every component of G − W has at least k vertices. The k -restricted edge connectivity is defined as the minimum cardinality over all k -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 k -restricted edge connectivity of a permutation graph is upper bounded by the so-called minimum k -edge degree. In this paper some sufficient conditions guaranteeing optimal k -restricted edge connectivity and super k -restricted edge connectivity for permutation graphs are presented for k = 2 , 3 .
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