Edge-fault diameter of C4-free graphs

Let G be a connected graph and k & ISIN; 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 5 k2+k+1 n + 9, 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 n2 on the 2-edge-fault diameter of 3-edge-connected graphs of order n not containing a 4-cycle.& COPY; 2023 Elsevier B.V. All rights reserved.