What is the maximum size of a clique?

What is the maximum size of a clique?

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.

Which has maximum clique size 2?

Explanation: the perfect bipartite graph has clique size 2.

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.

Can you have a clique of size 1?

Yes. We can have a clique of size 1 (the vertex itself) which comprises the entire graph and is connected to every other vertex (itself).

What is maximum 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.

How are clique numbers calculated?

To find a clique of G:

  1. Suppose that G has n vertices.
  2. Find a vertex v of the smallest possible degree in G.
  3. If the degree of v is n − 1, stop; G is a clique, so the largest clique in G has size n.
  4. Otherwise, remove v and all of its edges from G. Find the largest clique in the smaller graph.

How do I know my clique size k?

To find k-cliques we iterate the same method O(k) times. The method which finds the p+1-clique from p-clique takes O(n) time where n is number of vertices. So in overall the algorithm takes O(nk) time in the worst case.

What is a clique Mcq?

Concept: A clique is a subset of vertices of an undirected graph G such that every two distinct vertices in the clique are adjacent. Explanation: A clique in an undirected graph G = (V, E) is a subset of V i.e. V’ such that each pair of vertices in V’ is connected by an edge. A clique of size k is called k- clique.

Is maximum clique NP-Hard?

Because of the hardness of the decision problem, the problem of finding a maximum clique is also NP-hard. If one could solve it, one could also solve the decision problem, by comparing the size of the maximum clique to the size parameter given as input in the decision problem.

What is maximum Clique problem?