Stability and Robustness: Reliability in the World of Uncertainty

Case of two disjoint spanning treesThe Central TreeProblemHeuristics for theCTPFinal RemarksTheorem 1. Let T 1 and T 2 be two edge-disjoint spanning trees in the graphG = (V, E). Then dev s T ∗T≥ ⌈ ∗|V |−12⌉, where T ∗ is a central tree.In other words, theorem 1 states that if the graph contains twoedge-disjoint spanning trees, then the central tree has at most|V |−1⌊2⌋ edges in common with the maximally distant tree, or|V |−1equivalently, the robust spanning tree has at most ⌊2⌋edges in common with the corresponding minimum spanningtree in the worst-case scenario associated with T ∗ .Heuristics for the Central Tree Problem Yury Nikulin - p. 15/33