# On the tractability of the maximum clique problem

## TL;DR

This paper explores the theoretical possibility of a polynomial-time algorithm for the NP-complete maximum clique problem, providing a pseudo-code outline and analysis of its correctness and efficiency.

## Contribution

It presents a partially non-constructive proof of the existence of an exact polynomial-time algorithm for the maximum clique problem.

## Key findings

- Proof of existence of a polynomial-time algorithm
- Pseudo-code outline of the proposed algorithm
- Analysis confirming the algorithm's correctness and efficiency

## Abstract

The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm for this problem. We outline the algorithm in pseudo-code style. Then we prove its exactness and efficiency by analysis.

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Source: https://tomesphere.com/paper/1903.10700