I have to verify that a certificate to the Max-Clique problem. The Max-Clique: Given a graph G, find the largest clique (set of nodes such that all pairs in the set are neighbors).

The decision version of the Problem is: Does G have a clique of size K? Write a python program that takes a graph G, a number k and a possible certificate C to this problem.

Your program returns yes, if C is a clique of size k in the graph G and no otherwise. The graph is given in a file testGraph.txt. A file named cliqueList.txt is also given which contains group of possible cliques of vertices which you will need to check.

As part of this, you should request a k value from the user.

For example: program might do the following:

Enter the filename for graph: testGraph.txt

Please enter a value for k: 4

Enter the filename for possible cliques: cliqueList.txt

[2,3,4,5] : Yes

[1,2,3,6] : No

[1,2,3] : No

[1,3,6] : No

[0,1,5,6] : No

[1,2,3,4] : No