Network Augmentation and the Multigraph Conjecture
نویسنده
چکیده
Let Γ(n, m) denote the class of all graphs and multigraphs with n nodes and m edges. A central question in network reliability theory is the network augmentation problem: For G ∈ Γ(n, m) fixed, what H ∈ Γ(n, m + k) such that G ⊂ H is t-optimal, that is, maximizes the tree number t(H)? In the network synthesis problem, where G is the empty graph on n vertices, it is conjectured that all t-optimal graphs are simple. We demonstrate that, in the general network augmentation case, there exists an infinite class of non-empty G for which the resulting t-optimal augmentations are multigraphs. This conclusion has ramifications for future attempts to prove or disprove the multigraph conjecture for the network synthesis problem.
منابع مشابه
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