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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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Hardness of a special GAP-CLIQUE problem

In the GAP-CLIQUE$(k,\ell)$ problem, we are given a graph $G$ over $n$ vertices and have to decide whether $G$ contains a clique of size $k$ or no clique of size $\ell$. … In fact, even GAP-CLIQUE$(k,n^{\varepsilon - 1}k)$ is NP-hard. However, I am interested in GAP-CLIQUE instances, where $k$ and $\ell$ depend on the size of $G$. …
Dennis Kraft's user avatar