Finding Hamilton cycles in random graphs with few queries

We introduce a new setting of algorithmic problems in random graphs, studying the minimum number of queries one needs to ask about the adjacency between pairs of vertices of G(n, p) in order to typically find a subgraph possessing a given target property. We show that if p ≥ lnn+ln lnn+ω(1) n , then one can find a Hamilton cycle with high probability after exposing (1+o(1))n edges. Our result is tight in both p and the number of exposed edges.