Contractible Hamiltonian Cycles in Triangulated Surfaces

TL;DR

This paper establishes a necessary and sufficient condition for the existence of contractible Hamiltonian cycles in equivelar triangulations of surfaces, extending understanding of Hamiltonian properties in surface triangulations.

Contribution

It provides a complete characterization of when equivelar triangulations of surfaces contain contractible Hamiltonian cycles, a problem previously only partially understood.

Findings

Characterization of conditions for contractible Hamiltonian cycles

Extension of Hamiltonian cycle theory to equivelar surface triangulations

New criteria applicable to triangulations of various surfaces

Abstract

A triangulation of a surface is called $q$-equivelar if each of its vertices is incident with exactly $q$ triangles. In 1972 Altshuler had shown that an equivelar triangulation of torus has a Hamiltonian Circuit. Here we present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in equivelar triangulation of a surface.