Various Results on the Toughness of Graphs

We study the probabilistic longest path problem. We propose a modification strategy adapting a solution for a deterministic instance to a solution for the probabilistic one, we compute the functional associated with this strategy, and we evaluate the complexities of computing this functional and of computing the deterministic solution maximizing it. © 1999 John Wiley & Sons, Inc. Networks 33: 207-219, 1999