Polyhedra without cubic vertices are prism-hamiltonian

TL;DR

This paper proves that all 3-connected planar graphs with minimum degree at least four have a Hamiltonian prism, expanding understanding of Hamiltonian properties in polyhedral graphs.

Contribution

It establishes that polyhedral graphs with minimum degree four are prism-hamiltonian, a new result in graph theory linking degree conditions to Hamiltonian properties.

Findings

Polyhedral graphs with minimum degree ≥4 are prism-hamiltonian.

The result applies to all 3-connected planar graphs meeting the degree condition.

This advances the understanding of Hamiltonian cycles in graph products.

Abstract

The prism over a graph $G$ is the Cartesian product of $G$ with the complete graph on two vertices. A graph $G$ is prism-hamiltonian if the prism over $G$ is hamiltonian. We prove that every polyhedral graph (i.e. 3-connected planar graph) of minimum degree at least four is prism-hamiltonian.