Corrigendum to “Online purchasing under uncertainty”

In “Online purchasing under uncertainty” we proved theorems concerning the cost of purchasing var-ious combinatorial structures (paths, cycles, etc.) in graphs with randomly weighted edges, which are examined and either purchased or discarded one-at-a-time by the purchaser. We discussed three models (POM, ROM, AOM) according to whether the edges were presented in a purchaser-selected order, a random order, or an (adaptive) adversarially selected order. The statements of Theorems 1.6–1.11 claim O(1) upper bounds in all three models but the proofs presented apply only to the ROM and POM models; as such we withdraw the claims of the AOM upper bounds from these results.