Simple Necessary Conditions for the Existence of a Hamiltonian Path with Applications to Cactus Graphs

TL;DR

This paper presents necessary conditions for Hamiltonian paths in graphs, leading to a linear time algorithm for cactus graphs, with applications to molecular databases to identify traceable graphs.

Contribution

It introduces new necessary conditions for Hamiltonian paths and develops a linear time algorithm for cactus graphs, expanding tools for graph analysis.

Findings

Linear time algorithm for cactus graphs

Identified traceable graphs in molecular databases

Established necessary conditions for Hamiltonian paths

Abstract

We describe some necessary conditions for the existence of a Hamiltonian path in any graph (in other words, for a graph to be traceable). These conditions result in a linear time algorithm to decide the Hamiltonian path problem for cactus graphs. We apply this algorithm to several molecular databases to report the numbers of graphs that are traceable cactus graphs.