Computing Graph Properties by Randomized Subcube Partitions

We prove a new lower bound on the randomized decision tree complexity of monotone graph properties. For a monotone property A of graphs on n vertices, let p = p(A) denote the threshold probability of A, namely the value of p for which a random graph from G(n,p) has property A with probability 1/2. Then the expected number of queries made by any decision tree for A on such a random graph is at least Ω(n 2/ max{pn, logn}).

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