Contractible Hamiltonian cycles in triangulated surfaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 08 Jan 2014Embargo end date: 01 Jan 2010Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Elemente der Mathematik, volume 69, pages 23-29 (issn: 0013-6018, eissn: 1420-8962,

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Authors: Ashish Kumar Upadhyay;

doi: 10.4171/em/241 , 10.48550/arxiv.1003.5268 , 10.5169/seals-515854

arXiv: 1003.5268

Contractible Hamiltonian cycles in triangulated surfaces

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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.

6 pages, 1 figure

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Keywords

Computational Geometry (cs.CG), FOS: Computer and information sciences, Eulerian and Hamiltonian graphs, Geometric Topology (math.GT), Planar graphs; geometric and topological aspects of graph theory, 57Q15, 57M20, 57N05, Mathematics - Geometric Topology, Hamiltonian circuit, equivelar triangulation of torus, FOS: Mathematics, Computer Science - Computational Geometry, Mathematics - Combinatorics, Combinatorics (math.CO)

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