The edge fault-diameter of Cartesian graph bundles

A Cartesian graph bundle is a generalization of a graph covering and a Cartesian graph product. Let G be a k G -edge connected graph and D ̄ c ( G ) be the largest diameter of subgraphs of G obtained by deleting c < k G edges. We prove that D ̄ a + b + 1 ( G ) ≤ D ̄ a ( F ) + D ̄ b ( B ) + 1 if G is a graph bundle with fibre F over base B , a < k F , and b < k B . As an auxiliary result we prove that the edge-connectivity of graph bundle G is at least k F + k B .