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If the running time of an algorithm is upper constrained by a polynomial expression in the size of the method's input, the algorithm is said to be polynomial time.

Consider that $\text{P = NP}$, a $k-$clique is a clique that have k-nodes. Usually, a clique is in NP.

So, if $\text{P=NP}$ then clique is in P.

Therefore, if $\text{P=NP}$ , then clique is recognizable in polynomial time.

If $\text{P}=\text{NP}$, then $\text{°ä³¢±õ²Ï±«·¡âˆˆP}$ , and for each value of k , test whether $G$includes a clique of size $k$ in polynomial time.

Then find the size $t$ of a greatest clique in $G$ in polynomial time by checking if $G$ has a clique of each size from 1 to the number of nodes in $G$.

Find a clique with $t$ nodes as follows after knowing $t$ .

Remove each node ofG and determine the largest clique size that results.

Replace x and move on to the next node if the resultant size lowers.

If the final size is still , delete permanently and move on to the next node. When all nodes have been analysed in this way, the leftover nodes form a t -clique.

Therefore, the largest clique from the graph has been obtained.