A polynomial-time algorithm for the maximum clique problem
Zohreh Akbari · 2013
After more than six decades of its introduction, the maximum clique problem, which is one of the most applicable problems in the graph theory, has still no polynomial-time solution. This paper presents a polynomial-time algorithm for this problem, which detects the maximum clique of a given graph through a recursive approach. This polynomial solution to the clique problem, as an NP-complete problem, causes every problem in NP to have a polynomial solution, which leads to the equality of P and NP complexity classes.