The Complexity of Determining Existence a Hamiltonian Cycle is $O(n^3)$

TL;DR

This paper presents a new polynomial-time algorithm with complexity $O(n^3)$ for determining the existence of a Hamiltonian cycle in directed graphs by mapping the problem to a matching cover bipartite graph.

Contribution

It introduces a novel $O(n^3)$ algorithm for Hamiltonian cycle detection based on graph mapping techniques, improving understanding of the problem's complexity.

Findings

Hamiltonian cycle existence can be decided in $O(n^3)$ time.

Mapping to bipartite graphs provides a new approach for cycle detection.

The method offers potential for more efficient algorithms in graph theory.

Abstract

The Hamiltonian cycle problem in digraph is mapped into a matching cover bipartite graph. Based on this mapping, it is proved that determining existence a Hamiltonian cycle in graph is $O(n^3)$.