Edge-fault diameter of C₄-free graphs

Let G be a connected graph and k∈N. The k-edge-fault diameter of G is defined as the largest diameter of the graphs arising from G by deleting k edges. In this paper we show that the k-edge-fault diameter of a (k+1)-edge connected graph of order n not containing a 4-cycle cannot exceed [Formula presented], and we construct graphs that show that for k+1 a prime power this bound is close to optimal if k is large. For the special case k=2 we improve the above bound and obtain the sharp bound [Formula presented] on the 2-edge-fault diameter of 3-edge-connected graphs of order n not containing a 4-cycle.