# 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.