Searching for acyclic orientations of graphs Original Research Article

We want to find an unknown acyclic orientation O∗ of an (undirected) graph G by testing for certain edges how they are oriented according to O∗. How many tests do we need in the worst case? We give upper and lower bounds for this number c(G) in terms of the independence number of G and study the class of exhaustive graphs, i.e. graphs satisfying c(G) = |E(G)|. It is shown that there exist nonexhaustive graphs with arbitrarily large girth. The extremal exhaustive graphs are determined for n ⩾ 7.