Using the highest degree node as a pivot vertex optimizes the Bron-Kerbosch algorithm for this problem.
This problem can be solved in exponential time on d for a sparse, d-degenerate input, improving on a more common algorithm that takes exponential time on the size of the input. Considering the complement of the input to this problem allows one to show that this problem is reducible to the vertex-cover problem. Using the highest degree node as a pivot vertex optimizes the Bron-Kerbosch algorithm for this problem. Richard Karp nested this problem, (*) along with 3-SAT and 0-1 integer programming, directly below the Boolean satisfiability problem in his seminal 1972 paper "Reducibility among Combinatorial Problems". The brute force method of solving this problem generates all possible subgraphs and can be optimized by considering only the set of edges and only maximal subgraphs. For 10 points, name this NP-complete problem in graph theory that seeks to find the largest set of mutually adjacent vertices of a graph.
This problem can be solved in exponential time on d for a sparse, d-degenerate input, improving on a more common algorithm that takes exponential time on the size of the input.
maximum clique problem [or maximal clique problem]