What is Max-clique problem?

Max-Clique problem is a non-deterministic algorithm. In this algorithm, first we try to determine a set of k distinct vertices and then we try to test whether these vertices form a complete graph. There is no polynomial time deterministic algorithm to solve this problem. This problem is NP-Complete.

Which has maximum clique size?

The “maximum size clique” for a graph of n vertices is a clique of the largest size k (k ≤ n) such that there does not exist a clique of size k + 1 in the graph. A “maximal size clique for a vertex i” in a graph is the clique of the largest size that involves vertex i as one of the constituent vertices.

Is maximum clique NP-complete?

Therefore Max-Clique is NP-complete. An Independent Set in a graph is a set of nodes no two of which have an edge. E.g., in a 7-cycle, the largest independent set has size 3, and in the graph coloring problem, the set of nodes colored red is an independent set.

What is an example of a clique?

The definition of a clique is a small, closed off group of people. The popular group in high school is an example of a clique.

What is the largest clique in a graph?

The maximal clique is the complete subgraph of a given graph which contains the maximum number of nodes.

Is Max clique NP-complete?

What is clique decision problem?

Definition: In the field of computer science, the clique decision problem is a kind of computation problem for finding the cliques or the subsets of the vertices which when all of them are adjacent to each other are also called complete subgraphs.

Is maximal clique NP-hard?

The clique decision problem is NP-complete (one of Karp’s 21 NP-complete problems). The problem of finding the maximum clique is both fixed-parameter intractable and hard to approximate. And, listing all maximal cliques may require exponential time as there exist graphs with exponentially many maximal cliques.

Why is Max clique in NP?

Theorem 20.2 Max-Clique is NP-Complete. We then put an edge between two nodes if the partial assignments are consistent. Notice that the maximum possible clique size is m because there are no edges between any two nodes that correspond to the same clause c.