Characterization of graphs with infinite cyclic edge connectivity (Q2483391)

In the paper is given a characterization of connected graphs without a cyclic edge cutset. Let \(G\) be a connected graph. A cyclic edge cutset is an edge cutset whose deletion disconnects the graph such that two of the components contain cycles. The cyclic connectivity \(c\lambda(G)\) is the minimum cardinality of a cyclic edge set. It is given a characterization of graphs with finite cyclic edge connectivity in terms of the minimal degree and the girth of a graph. An efficient algorithm for decision whether graph \(G\) has a finite cyclic edge connectivity is presented.