Generating punctured surface triangulations with degree at least 4-Reference-Cited by-同舟云学术

Generating punctured surface triangulations with degree at least 4

Published:2022-02-01 Issue:1 Volume:30 Page:129-151
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Chávez María-José¹,Negami Seiya²,Quintero Antonio³,Villar-Liñán María Trinidad³

Affiliation:

1. Departamento de Matemática Aplicada I , Universidad de Sevilla , Spain

2. Faculty of Environment and Information Sciences , Yokohama National University , 79-2 Tokiwadai, Hodogaya-Ku , Yokohama , Japan .

3. Departamento de Geometría y Topología , Universidad de Sevilla , Spain

Abstract

Abstract As a sequel of a previous paper by the authors, we present here a generating theorem for the family of triangulations of an arbitrary punctured surface with vertex degree ≥ 4. The method is based on a series of reversible operations termed reductions which lead to a minimal set of triangulations in such a way that all intermediate triangulations throughout the reduction process remain within the family. Besides contractible edges and octahedra, the reduction operations act on two new configurations near the surface boundary named quasi-octahedra and N-components. It is also observed that another configuration called M-component remains unaltered under any sequence of reduction operations. We show that one gets rid of M-components by flipping appropriate edges.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2022-0008

Reference24 articles.

1. [1] D.W. Barnette, A. L. Edelson, All 2−manifolds have finitely many minimal triangulations, Israel J. Math. 67 (1989), 123-128.10.1007/BF02764905

2. [2] G. Brinkmann, B. D McKay Fast generation of planar graphs, MATCH Commun. Math. Comput. Chem. 58(2) (2007), 323-357.

3. [3] A. Boulch, É. Colin de Verdière, A. Nakamoto, Irreducible triangulations of surfaces with boundary, Graphs Comb., 29 No. 6 (2013), 1675–1688.

4. [4] M.J. Chávez, S. Lawrencenko, A. Quintero, M. T. Villar, Irreducible triangulations of the Möbius band, Bul. Acad. Sţiinţe Repub. Mold. Mat., No. 2(75) (2014), 44–50.

5. [5] M.J. Chávez, S. Negami, A. Quintero, M. T. Villar, Generating families of surface triangulations. The case of punctured surfaces with inner degree at least 4. arXiv e-print service, Cornell University Library, http://arxiv.org/abs/1507.03975v2, (2015).