Molecular solutions for the Maximum K-colourable Sub graph Problem in Adleman-Lipton model

TL;DR

This paper presents a DNA-based algorithm within the Adleman-Lipton model that solves the NP-hard Maximum k-colourable Subgraph problem in polynomial time, extending DNA computing applications to complex graph problems.

Contribution

It introduces a novel DNA algorithm for the NP-hard Maximum k-colourable Subgraph problem using the Adleman-Lipton model, achieving polynomial-time solutions.

Findings

DNA algorithm solves Maximum k-colourable Subgraph in polynomial time

Extends DNA computing to NP-hard graph problems

Demonstrates feasibility of molecular solutions for complex computational problems

Abstract

Adleman showed that deoxyribonucleic acid DNA strands could be employed towards calculating solutions to an instance of the Hamiltonian path problem . Lipton also demonstrated that Adleman techniques could be used to solve the Satisfiability problem. In this paper, we use Adleman Lipton model for developing a DNA algorithm to solve Maximum k-colourable Sub graph problem. In spite of the NP-hardness of Maximum k-colourable Sub graph problem our DNA procedures is done in a polynomial time.