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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.

3 votes

Clique-problem for planar graph

Now, if some graph had a clique of size $5$, by taking this clique as a subgraph we would have that the complete graph on $5$ vertices $K_5$ is planar. … Thus, $K_5$ is not planar and our original graph has no clique of size $5$ or more. …
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Prove "Vertex Cover OR Clique" is NP complete

You can easily reduce from clique as follows. … Now, $G$ has a clique of size $\geq k$ if and only if $G'$ has a clique of size $\geq k$. …
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