Contractible Hamiltonian Cycles in Polyhedral Maps

TL;DR

This paper establishes a precise condition for the existence of contractible Hamiltonian cycles in equivelar maps on surfaces and provides an algorithm for their construction, extending the results to more general maps.

Contribution

It introduces a necessary and sufficient condition for contractible Hamiltonian cycles and presents a construction algorithm, generalizing previous results.

Findings

Condition for existence of contractible Hamiltonian cycles

Algorithm for constructing such cycles

Generalization to broader classes of maps

Abstract

We present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in the edge graph of equivelar maps on surfaces. We also present an algorithm to construct such cycles. This is further generalized and shown to hold for more general maps.