Clique (from WikiPedia):
Clique is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete.
K-Clique problem: Finding a clique of size K. This is NP-complete according to Wiki,
Cliques have also been studied in computer science: finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result many algorithms for finding cliques have been studied.
Let us consider a "constrained k-clique problem" - which is a k-clique problem with a constraint of having a predetermined vertex included in the solution. What would be the complexity of this problem? Is it a known problem in the literature?