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A clique is a subset of the vertices of a graph such that every pair of vertices in the subset is connected by an edge.

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Why is EXACT-CLIQUE not in co-NP?

In my lecture I saw the problem of $\text{EXACT-CLIQUE} = \{\langle G,k\rangle : \text{the largest clique in $G$ is of order $k$}\}$ I understand this problem is obviously not in NP as we would need … Because we could simply use non-determinism to guess a clique bigger than $k$ and then check if it indeed makes a clique. …