How can you perform the clique decision algorithm fewer than $ O(n) $ times to solve clique optimization?
I'm not sure if my approach is right but this is my thought process: you would pick vertices in a graph and see if they form a clique, then keep picking more vertices until you have the max possible clique.
I'm not sure how it can be done less than $ O(n) $ times.
I can imagine an undirected graph such as:
where $ \{A, B, C\} $ and $ \{B, C, D\} $ would be cliques. The number of vertices is 4, and the number of vertices in the cliques is 3, which is $ n - 1 $. Would this count as being done in less than $ O(n) $ times, or is this the wrong approach to this problem?