A Polynomial Time Algorithm for the Hamilton Circuit Problem

TL;DR

This paper presents a polynomial-time algorithm for the Hamilton Circuit problem by reducing it to a new MSP problem, which is also shown to be NP-complete, implying NP=P.

Contribution

It introduces the MSP problem and demonstrates a polynomial reduction from HC, along with a polynomial algorithm for MSP, challenging existing NP-completeness assumptions.

Findings

Hamilton Circuit problem reduced to MSP problem

Proposed polynomial algorithm for MSP problem

Implication that NP=P

Abstract

In this paper, we introduce a so-called Multistage graph Simple Path (MSP) problem and show that the Hamilton Circuit (HC) problem can be polynomially reducible to the MSP problem. To solve the MSP problem, we propose a polynomial algorithm and prove its NP-completeness. Our result implies NP=P.