Improved upper bounds for vertex and edge fault diameters of Cartesian graph bundles

Mixed fault diameter of a graph G, D(a,b)(G), is the maximal diameter of G after deletion of any a vertices and any b edges. Special cases are the (vertex) fault diameter D a = D(a,0) and the edge fault diameter D E a = D(0,a). Let G be a Cartesian graph bundle with fibre F over the base graph B. We show that (1) D a+b+1(G) ≤ D V a (F )+D V b (B) when the graphs F and B are kF -connected and kB-connected, 0 < a < kF , 0 < b < kB , and provided that D(a−1,1)(F ) ≤ D V a (F ) and D(b−1,1)(B) ≤ D V b (B) and (2) D a+b+1(G) ≤ D E a (F ) + D E b (B) when the graphs F and B are kF -edge connected and kB-edge connected, 0 ≤ a < kF , 0 ≤ b < kB , and provided that D a (F ) ≥ 2 and D E b (B) ≥ 2.