Triangulated map with minimum degree four is Hamiltonian

TL;DR

This paper proves that any triangulated map with a minimum degree of four contains a contractible Hamiltonian cycle, advancing understanding of Hamiltonian cycles in surface-embedded graphs.

Contribution

It establishes the existence of contractible Hamiltonian cycles in triangulated maps with minimum degree four, a new result in topological graph theory.

Findings

Existence of contractible Hamiltonian cycle in triangulated maps with minimum degree four

Extension of Hamiltonian cycle theory to surface-embedded graphs

New conditions for Hamiltonicity in triangulated maps

Abstract

A $triangulation$ is an embedding of a graph on surfaces where every face has length three. In this article, we show the existence of contractible Hamiltonian cycle in triangulated maps of which minimum degree is four.