The Hamiltonian properties of rectangular meshes with at most two faulty nodes

TL;DR

This paper addresses the Hamilton cycle problem in rectangular meshes with up to two faulty nodes, providing a polynomial-time algorithm and a novel approach distinct from previous methods.

Contribution

It introduces a new method for solving the Hamilton cycle problem in faulty rectangular meshes, demonstrating polynomial-time solvability.

Findings

Hamilton cycle problem is solvable in polynomial time for meshes with up to two faulty nodes.

A new approach differs from earlier methods, improving problem-solving techniques.

The paper provides an algorithmic solution with theoretical guarantees.

Abstract

In this paper we consider the Hamilton cycle problem in the rectangular meshes with at most two faulty nodes.We prove that this problem is solvable in polynomial time with a corresponding algorithm. We provided an entirely new approach to this problem being different from the method early used on this problem.