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Questions about the hardest problems in NP, i.e. of those that can be solved in polynomial time by nondeterministic Turing machines.

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Graph contains two disjoint cliques

To correct the reduction(by @Nathaniel suggestion), we address the issue that arises when $k = |V|$ (the size of the vertex set of $G$). In this case, the entire graph is a single clique, so it is …
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Graph contains two disjoint cliques

Is $$\text{2disjCLIQUEs} = \left\{ \langle G, k_1, k_2 \rangle : \text{ the graph $G$ contains two disjoint cliques,one of size $k_1$, and the other of size $k_2$}\right\}$$ in $\texttt{P}$ or $\text …