on the edge-connectivity of c4-free graphs

Let g be a connected graph of order n and minimum degree δ(g). the edge-connectivity λ(g) of g is the minimum number of edges whose removal renders g disconnected. it is well-known that λ(g)≤δ(g), and if λ(g)=δ(g), then g is said to be maximally edge-connected. a classical result by chartrand gives the sufficient condition δ(g)≥n−1/2 for a graph to be maximally edge-connected. we give lower bounds on the edge-connectivity of graphs not containing 4-cycles that imply that for graphs not containing a 4-cycle chartrand's condition can be relaxed to δ(g)≥√n/2+1, and if the graph also contains no 5-cycle, or if it has girth at least six, then this condition can be relaxed further, by a factor of approximately √2. we construct graphs to show that for an infinite number of values of n both sufficient conditions are best possible apart from a small additive constant.