Explicit construction of linear sized tolerant networks

For every ϵ>0ϵ>0 and every integer m>0m>0, we construct explicitly graphs with O(m/ϵ)O(m/ϵ) vertices and maximum degree O(1/ϵ2)O(1/ϵ2), such that after removing any (1-ϵ)(1-ϵ) portion of their vertices or edges, the remaining graph still contains a path of length m. This settles a problem of Rosenberg, which was motivated by the study of fault tolerant linear arrays.