Finding and certifying a large hidden clique in a semirandom graph

Alon, Krivelevich and Sudakov (Random Structures and Algorithms, 1998) designed an algorithm based on spectral techniques that almost surely nds a clique of size (p n) hidden in an otherwise random graph. We show that a diierent algorithm, based on the Lovv asz theta function, almost surely both nds the hidden clique and certiies its optimality. Our algorithm has an additional advantage of being more robust: it also works in a semi-random hidden clique model, in which an adversary can remove edges from the random portion of the graph.