Is it possible to find the maximum clique in general graphs?

TL;DR

This paper introduces two algorithms for finding the maximum clique in graphs, one effective for special cases and another with execution time bounded by the number of cliques per vertex, addressing a computationally hard problem.

Contribution

It presents two novel algorithms for maximum clique detection, with one tailored for specific cases and the other with a bounded execution time based on clique counts.

Findings

First algorithm finds maximum clique in some special cases.

Second algorithm's runtime is bounded by clique counts per vertex.

Provides efficient approaches for a computationally hard problem.

Abstract

Finding the maximum clique is a known NP-Complete problem and it is also hard to approximate. This work proposes two efficient algorithms to obtain it. Nevertheless, the first one is able to fins the maximum for some special cases, while the second one has its execution time bounded by the number of cliques that each vertex belongs to.