On the Aanderaa-Rosenberg Conjecture

In a recent paper [1], Rosenberg conjectures that the results found in Holt and Reingold [2], can be generalized. Suppose that graphs are presented via their adjacency matrices. Then Holt and Reingold show that any algorithm which detects whether or not a graph is strongly connected (respectively, contains a cycle) must in worst case probe 0(n2) entries of the given n x n adjacency matrix. Rosenberg then considers restrictions on graph property P such that any algorithm takes in worst case 0(n2) probes to determine whether or not a n-node graph has property P.